Can an unarmed paladin work?

So I'm wanting to play a paladin character who without armor for backstory reasons and was wondering what I could do to make that character work. I know that multi-classing into warlock works, but I kind of don't want to multitask this time. So is there any other options or better multi-classes cuz they also don't really want to use warlock. 

But if warlock is the best option, is there a way to do a more paladin focused paladin warlock multiclass. Oh and also, I am trying to do a good aligned paladin so something like oath of devotion or other such paths.

Unarmed (no weapons) or unarmored (no armor) or both?  

You can probably hammer any of those square pegs into the round hole, provided the party isn't overly optimized.  Assuming I am understanding correctly that you are mostly trying to avoid armor, it can be done though it won't be "good"  Push dex to get your AC as high as possible...assuming you can still use weapons to take a rapier.  Take arcane initiate so you can get mage armor, those two should give you a 16 AC out of the box.  Can you use a shield?  Or reflavor something to give a shield's AC benefit, such as wrapping your cloak around your arm and using it as a parrying device.  That would get you to 18ish at level 1.

You could try to pick up mobile and try to move in, and out of combat to avoid being attacked.  Defensive Duelist might be an option as well.

EDIT:  If old feats are in play, perhaps your DM will let you take eldritch adept and get mage armor via that invocation.  https://www.dndbeyond.com/feats/451339-eldritch-adept

I'm thinking that would be kind of tough. For one, you'd want to boost DEX if you aren't wearing armor. Except your unarmed strikes would use STR and you don't really have a way to change that. And then you'd want CHA for your aura and spellcasting... It just is too MAD, I'd think, at least as a pure class paladin. I just think you are giving up a lot of paladin features (heavy armor, martial weapons, and optimization in one of your main stats) to play this. Do you think you could reflavor a monk to devote themselves to an oath like a paladin, but have all the monk features?

go monk. raidiant strikes works with unarmed strikes if you get there. so does crusader's mantle.