I noticed the skill Hand-to-Hand skill. Could I go through the game being a bare-knuckle fist fighter? Or do you think it'd be to hard?

I havent done it before, but i think it'd be ok. If im not wrong many people have done that, as some kind of "monk" class
Anyway if anything goes wrong, im betting that enchanting can certainly help.

There are folks who successfully play H2H characters.

The drawbacks are notable: No poison, no enchantments, lower damage, short range.

The perks are a fast attack rate and that your fists will damage the victim's fatigue. If their fatigue goes below zero, they will fall to the ground and stay there, helpless, until their fatigue goes above zero. It would seem that learning some complementary spells that damage/drain fatigue could help get some good mileage out the fatigue damage.

Because your damage is lower, you might consider 'capping' your character somewhere between 20-30 so foes don't continue to grow into ever bigger hitpoint pools.

Because you are likely to often be engaged in extended melee, some attention to defense would seem prudent.