In the martial arts feature the last paragraph states:

Certain monasteries use specialized forms of the monk weapons. For example, you might use a club that is two lengths of wood connected by a short chain (called a nunchaku) or a sickle with a shorter, straighter blade (called a kama). Whatever name you use for a monk weapon, you can use the game statistics provided for the weapon.

With this you could make any assortment of fun weapons to suit your Monk's theme. With Martial Arts damage dice chances are whatever you come up with will not exceed the Quarterstaff's or Spear's damage or utility. However what happens if you make a fist styled weapon? There are tons of such weapons in history such as the Deer Horn Knives, Bagh Nakh Tiger Claws, Cestus, Katar, Punch Daggers, etc.. If you were to flurry of blows with these monk weapons equipped would you make all strikes with these weapons or have to make the last two strikes with your legs, knees, elbows, etc.? If you can make a "unarmed strike" with a fist weapon can you reap the benefits from a magical enchantment such as the Artificer's Enhanced Weapon or Radiant Weapon Infusions? ie. + to attack rolls and damage rolls with "unarmed strikes"

Quote from cgrandall2 >>

In the martial arts feature the last paragraph states:

Certain monasteries use specialized forms of the monk weapons. For example, you might use a club that is two lengths of wood connected by a short chain (called a nunchaku) or a sickle with a shorter, straighter blade (called a kama). Whatever name you use for a monk weapon, you can use the game statistics provided for the weapon.

With this you could make any assortment of fun weapons to suit your Monk's theme. With Martial Arts damage dice chances are whatever you come up with will not exceed the Quarterstaff's or Spear's damage or utility. However what happens if you make a fist styled weapon? There are tons of such weapons in history such as the Deer Horn Knives, Bagh Nakh Tiger Claws, Cestus, Katar, Punch Daggers, etc.. If you were to flurry of blows with these monk weapons equipped would you make all strikes with these weapons or have to make the last two strikes with your legs, knees, elbows, etc.? If you can make a "unarmed strike" with a fist weapon can you reap the benefits from a magical enchantment such as the Artificer's Enhanced Weapon or Radiant Weapon Infusions? ie. + to attack rolls and damage rolls with "unarmed strikes"

 RAW, no. Your unarmed strikes made as part of flurry of blows cannot benefit from weapon properties and would be assumed to be legs, knees, elbows, etc as you stated 

What Kaboom said. Reflavouring martial arts weapons is just that, reflavouring weapons. It allows you to turn a club into nunchuks or a handaxe (or sickle) into a kama. It doesn't allow you to turn your knee into a weapon that can be infused by an artificer.

Personally, I don't see any issue with reflavoring your unarmed strikes as strikes with your weapons. Reflavouring changes nothing about the type of damage nor to the bonuses on the rolls. I often think of my Tabaxi Monk's unarmed strikes as being from the hafts of his weapons (twin yklwas), and his claws attacks being slashes with the blades. These attacks don't benefit from the yklwas magical bonuses; it's just the flavor of the attacks.

Now, if you convinced your DM to give out items that gave bonuses specifically to your unarmed strikes, your bonus attacks would benefit (and your main attacks if you were using unarmed attacks). The Tabaxi's claws come to mind; allowing my Monk to do bludgeoning or slashing damage with my unarmed strikes.

Quote from zeekec >>

Personally, I don't see any issue with reflavoring your unarmed strikes as strikes with your weapons. Reflavouring changes nothing about the type of damage nor to the bonuses on the rolls. I often think of my Tabaxi Monk's unarmed strikes as being from the hafts of his weapons (twin yklwas), and his claws attacks being slashes with the blades. These attacks don't benefit from the yklwas magical bonuses; it's just the flavor of the attacks.

Now, if you convinced your DM to give out items that gave bonuses specifically to your unarmed strikes, your bonus attacks would benefit (and your main attacks if you were using unarmed attacks). The Tabaxi's claws come to mind; allowing my Monk to do bludgeoning or slashing damage with my unarmed strikes.

 I am a big fan of the rule of cool over stat advantage. I just didn't know if this had been addressed officially and answered. Looking back at it though it seems pretty clear that it's intended to be unarmed strikes with a big period.

I'll personally recommend a magic item 'Eldritch Claw Tattoo' from the sourcebook 'Tasha's Cauldron of Everything'. It enhances the efficiency of the Unarmed Strike and functions as a 'Fist Weapon' that's been quoted below:

"Magical Strikes: While the tattoo is on your skin, your unarmed strikes are considered magical for the purpose of overcoming immunity and resistance to nonmagical attacks, and you gain a +1 bonus to attack and damage rolls with unarmed strikes." - Page 126

Besides, I'd consider the 'Fist Weapons' that you mentioned in your post as 'Improvised Weapon', do check out the rule regarding the use of an improvised item/weapon.

Curious, if you crossclass into rogue do your unarmed strikes count for sneak attacks? They use Dex like finesse weapons do

Quote from Starscream45 >>

Curious, if you crossclass into rogue do your unarmed strikes count for sneak attacks? They use Dex like finesse weapons do

 Nope. Although martial arts allows you to use Dex your unarmed strikes do not have the weapon property of finesse. So they don’t qualify. 

kind of like, shadow monks and four elements monks can cast spells, but they are not either the spellcasting or pact magic features so they do not qualify for the Eldritch Adept feat. 

It’s like  finesse but it isn’t actually finesse

Quote from ThriKreenWarrior >>

Quote from Starscream45 >>

Curious, if you crossclass into rogue do your unarmed strikes count for sneak attacks? They use Dex like finesse weapons do

 Nope. Although martial arts allows you to use Dex your unarmed strikes do not have the weapon property of finesse. So they don’t qualify. 

kind of like, shadow monks and four elements monks can cast spells, but they are not either the spellcasting or pact magic features so they do not qualify for the Eldritch Adept feat. 

It’s like  finesse but it isn’t actually finesse

 Gotcha, in that case, how would you flavor metal claws like Black Panther or Cat Woman etc. Daggers?

Quote from Starscream45 >>

Quote from ThriKreenWarrior >>

Quote from Starscream45 >>

Curious, if you crossclass into rogue do your unarmed strikes count for sneak attacks? They use Dex like finesse weapons do

 Nope. Although martial arts allows you to use Dex your unarmed strikes do not have the weapon property of finesse. So they don’t qualify. 

kind of like, shadow monks and four elements monks can cast spells, but they are not either the spellcasting or pact magic features so they do not qualify for the Eldritch Adept feat. 

It’s like  finesse but it isn’t actually finesse

 Gotcha, in that case, how would you flavor metal claws like Black Panther or Cat Woman etc. Daggers?

 That would probably be the best way to go. But check with your DM. 

For Tabaxi and Tortles, how would you handle their claw attacks?  Are they unarmed attacks, but with a different damage type?  That’s what I was hoping.

Quote from Sisyphus_Rocks >>

For Tabaxi and Tortles, how would you handle their claw attacks?  Are they unarmed attacks, but with a different damage type?  That’s what I was hoping.

 Racial weapons are just a modification of the type of damage for unarmed strikes. They can turn BA and flurry of blows attacks from bludgeoning to their appropriate type. usually slashing I believe.

Although not granting bonuses to all attacks it seems completely plausible and within the rules to use fist styled monk weapons to proc other abilities. Sneak attack for instance or spells such as Booming Blade or Green-Flame Blade. 

Quote from cgrandall2 >>

Although not granting bonuses to all attacks it seems completely plausible and within the rules to use fist styled monk weapons to proc other abilities. Sneak attack for instance or spells such as Booming Blade or Green-Flame Blade. 

 As long as the fist weapon was finesse and you met other sneak attack requirements it should work with DM approval. Wouldn’t work on Bonus Action attack or FoB by rules. Also GFB and BB don’t use attack action so yes you could use fist weapon with spell but not your martial arts so you would have just the one attack with those cantrips. 

Since you used an attack with GFB or BB could you use the optional monk features Focused Aim in the event that you miss to boost your attack thus procing Ki-Fueled Attack to give you an additional attack as a bonus action?

That actually should work as you meet the requirements, as far as I can tell.