Okay, so I like Hexblade Warlocks as much as the next guy, and am currently playing a Changeling Hexblade Bladepact Warlock and enjoying it a ton. However, I do think that their spell list is a bit weird (I've never really liked how Warlocks get an expanded spell list, but not spells known, but that's neither here nor there). Here it is:

Hexblade Expanded Spells

Let's go down the spells one by one:

1. Shield. Okay. It's a good spell, but due to the fact that it takes up literally half of your spells known at level 1 and your only spell slot (and half your spell slots from level 2-10) to temporarily increase your AC, it doesn't seem like a good spell to give Warlocks. Especially given the fact that the vast majority of Hexblades will become Bladepact Warlocks, and once you get access to Eldritch Smite, you literally have too few spell slots going around to even consider using this spell most of the time. 
2. Wrathful Smite. This spell sucks, for practically everyone but Conquest Paladins. It is especially bad for warlocks. I mean, almost every warlock takes hex, and this deals the same amount of damage, but only once, while also taking concentration! I mean, I understand wanting to allow warlocks to smite, but this is not a good way to do so.
3. Blur. Absolutely nothing about the description of this subclass describes them as using illusion magic or being able to blur like this. Not only does it not fit the theme that well, but it also takes concentration, and is strictly worse than mirror image. If they wanted to let hexblades blur themselves, possibly like a ghost being phantasmal, I'm perfectly fine with that, but they gave no explanation and instead gave a spell that will likely never, ever be used by a Hexblade warlock a single time in the campaign. 
4. Branding Smite. So, wait? I understand smiting, but why this smite? Not only does it make people not be invisible (which seems contradictory with the theme of the subclass), but it deals radiant damage (not very fitting in the theme), makes them glow (again, not fitting), and also has the same as literally every other smite spell in the game. It's concentration, and in the long run (as in, once you get Thirsting Blade and attack twice on your turn), hex will be way, way, way, way, way better than this spell. 
5. Blink. Okay, ghost connected. I'm kind of confused as to why this subclass that is connected to a cursing sentient weapon/raven queen lets us be like a ghost, but I'll allow the lazy development for the sake of this spell. I like this spell and have made use of it multiple times as a Changeling Hexblade for infiltration and ignoring attacks. It is an action to cast, but it's worth the 50% chance of literally being un-targetable by your enemies. I'm fine with this spell, but only when you suspend your disbelief a bit. 
6. Elemental Weapon. Unless you have a very lenient DM, you will likely never make use of this spell a single time in the campaign. The vast majority of Hexblade characters will be Pact of the Blade Warlocks, which will always give you a magic weapon, and since this spell infuriatingly cannot be used on a magic weapon, you will almost never be able to use it. Even if you did, it doesn't do more average damage than hex until your spell slots become 5th level (so, at level 9 for you), and even once they do, elemental damage is extremely more likely to be immune to/resisted than the necrotic damage hex does. This spell sucks for most people, but especially Hexblade warlocks. 
7. Phantasmal Killer. No real complaints, but this spell will probably not be used a ton for hexblades who are normally concentrating on hex. It's a good spell, but it just is not likely to get a ton of use. 
8. Staggering Smite. Again, in the long run, this spell is worse than hex. It is only worthwhile if you know you can get a critical hit (through hold person or a diviner). 
9. Banishing Smite. This is okay, I guess, but only fits the theme of "smiting," which isn't even explained beyond them being able to use magic and weapons. Again, most often your concentration will be taken up by Hex, but this can be more worthwhile in some circumstances. 
10. Cone of Cold. Wtf is this? How the hell does this fit the theme of this subclass whatsoever? The lazy "theme" of this subclass has taken so much of my suspension of disbelief at this point that I am no longer forgiving this good spell being on their spell list. This is a good spell, but makes no sense whatsoever for warlocks. I mean, seriously! WotC couldn't think of anything better than this? 

Suggestions to replace them:

1. Absorb Elements. It fits the theme of melee attacking and possibly could be explained as temporarily going ethereal to reduce damage. It still has the same problem that almost every other warlock spell in the game has, but is better than shield, IMO. 
2. Dissonant Whispers, maybe? Edit: Changed from Unseen Servant, not noticing that it was already on the Warlock spell list. 
3. See Invisibility? 
4. Phantasmal Force
5. The current spell is good.
6. Bestow Curse or Haste or Phantom Steed
7. The current spell is fine. 
8. Greater Invisibility, maybe. 
9. Dominate Person or Geas
10. Steel Wind Strike, probably. Maybe Seeming.

That's my thoughts. Anyone feel the same about some/all of them? Anyone disagree with some/all of them? I'm excited to hear your responses. 

Branding Smite and Banishing Smite are the only two smite spells that can be used through a ranged weapon, so if you want to make a bowman Hexblade they can add a bit of damage there. 5D10 force damage that also banishes the target if it's under 50 wounds is significantly better than D6 necrotic damage per hit. The principle of them being concentration and bonus action spells is you pick a target, use your bonus action to cast the spell, then loose. If you have improved pact weapon (longbow) and thirsting blade (double attacks with pact weapon) you have two chances to land the shot.

Shield is a trap for Warlocks, since you only have two spell slots most of the time, but it is good for multiclassing from Bards who don't get it innately.

Unseen Servant is already a Warlock spell. 

The smite spells were added to give a Paladin feel to a a quasi-Paladin character, but I agree most of them aren't very good (Paladins don't use them either).

But yes, the Hexblade spell list is pretty bad, but that seems to be the way with most additional spell lists (just look at Oath of the Ancients Paladin). Haste would be nice.

Unless there is a specific expanded description of the Hexblade subclass, it's is really quite open-ended. The Shadowfell has a few different cosmologies, and among them, the Shadow Weave empowers Enchantment, Illusion, and Necromancy spells, so a pretty good case for any individual spell can be made, even if the full list doesn't necessarily make sense together.

However, the Hexblade's "function", if not it's "flavor", is combat.

Smite spells, and defensive spells are all intimately tied to the functionality of the Hexblade. Reflavoring them to suit the specific patron/origin is easy enough. Swapping them out for the spells you suggest makes sense for the "flavor", but not so much for the "function".

Cone of Cold is definitely a little weird, but cold is often associated with undead and Warlocks already have access to a lot of the better options. If I were to swap it out with anything, I'd probably choose Steel Wind Strike as a melee "AoE".

I had thought about Steel Wind Strike, but it is already on the Warlock spell list.

Edit: Never mind, I apparently read that wrong. It is not.

According to the spell description it's only available to Rangers and Wizards. Maybe it was mis-tagged.

edit: Acknowledging the above edit.

I stumbled upon this thread, because I too agree that the Hexblade exapnaded spell list could be improved, there were alot of great choices in this thread that influcned this list I put togther. I mainly focused on Gishy weapon soundy spells with some nonconcentration options, I also kept half of the original options because I think they still work decent and are on theme with the Hexblade. 

Of course I added Steel wind Strike to my attempt at Revised Hexblade Exapanded spell list, its litrally an anime super move.  

 Edit: Switched out Phantasmal Force for Tasha's Mind Whip, felt that Mind whip functions similarly but without Concentration which is always a plus for Hexblade. Replaced Shield with Inflict wounds (aka cleric Smite). Now it has variety with spells relating to multiple classes instead of mostly paladin: two from Paladin,two from Ranger, two from cleric,two from sorcerer and two from wizard. 

Quote from The_Leviathan_of_Levistus >>

1. Shield. You're only supposed to take this at the 1st few lvls.  At that stage any hit could be fatal as you have warlock HD, and can be easily one shot by a ambusing bears bite or something similar.  At those early levels when you havent had gold to get medium armour or shields you'd be proficient in, you usually start with just leather armour.  The difference between 11+Dex and 16+Dex is staggering.  You can freely swap out of using this spell later when you lvl up more or get better gear.
2. Wrathful Smite. Think situationally.  If your foe is undead, they're 95% of the time immune to necrotic.  Psychic damage is the least resisted damage type in the game.  Also fear is a very potent debuff in a duel.  Disadvantage on all ability checks and attacks on everyone from the fear can also make a big difference if theres one problematic foe you need to weaken.  If you're foe is a rogue its 100% removal of their sneak attack damage.  Finally ranged warlocks will be able to disengage and resume sniping as they wont be able to move closer, giving positional CC advantage.
3. Blur. Classic melee defense buff.  Makes sense on a usually melee warlock subclass.  Similar advantages to fear for the disadvantages, but applies disadvantage to all foes against only you as supposed to all attacks from one foe on everyone.  A strong option before you have access to Shadow of Moil.
4. Branding Smite. Amazing spell.  Have it on Battlesmith.  One of only 2 ranged smites.  For bow based Hexblades.
5. Blink.
6. Elemental Weapon. Target touch. What does more damage at high levels, you hitting twice with your sword, or the fighter hitting 3+ times with their greataxe... And then action surging?  Also If you're a melee warlock and you're being attacked by a flying mage, you can cast this on a non-magical backup bow.  Flexible elemental damage so for foes with vilnerabilities (like a treant, or various kinds of undead usually immune to hex necrotic) has some uses there.  Mostly though you should be taking this if you want to be the kind of warlock who buffs their allies.
7. Phantasmal Killer. Terrible spell.  I'm just biased against save or do nothing spells, particularly on warlocks who only ever have 2 spells for 50% their life.  It has TWO chances to do no damage as they need to fail 2 back to back saves so its basicly casting with disadvantage already.  Take only for RP flavour.  TECHNICALLY could do high DPS for no action over multiple rounds... If they have a terrible willpower save. 
8. Staggering Smite. Only here cos its a smite.  Not a good one.  On the plus side it is psychic damage the best kind, and you might make a mage unable to counterspell.
9. Banishing Smite. Best ranged smite in the game.  High force damage, and CC.  Remove a threat for a minute (possibly permanently) as per banish, but you get to damage it first a lot.
10. Cone of Cold.  ... ok this is a little odd, but Its 8d8 compared to synaptic statics 8d6, and makes cool ice statues, pun intended!  Nice given one of the nine hells is a frozen wasteland though... and for a frosty themed warlock its a welcome addition.  Tomb of levistus, lance of lethargy, Armour of agathys, investiture of ice, Elemental bane...
    Warlocks don't get too many AOE options with decent damage.  Its nice to have another option.  Arguably wall fo light would be better, but it just might not fit your theme.

 My 2 cents on the topic.