What perks exactly could you have? There aren't as many things as in other perk trees.
Well, assuming Unarmed made it as a skill, it would require the ability to guard like it did previously. Perhaps instead of Unarmed blocking being a part of the Block skill, they could have gave Unarmed it's own type of blocking that is within the Unarmed tree. It would definitely make more sense as it's more martial arts rather than blocking with a weapon/shield.
Perhaps while guarding (LT) you can press RT to elbow your enemy, which would be akin to shield bashing and make the enemy flinch/do some damage?
Some ideas:
20/40/60/80/100% more damage.
Power Attacks cost 25% less stamina.
Standing Power Attack does 25% bonus damage with a chance to.....break you enemy's jaw? or snap their neck? Something akin to decapitating like One/Two-handed trees have.
Can do a power attack while sprinting that does double critical damage.
(All of the above are just what One/Two-handed have.)
Attacks are x% (not sure by how much honestly) faster.
Attacks have a 10% chance of paralyzing the enemy for 3 seconds.
Maybe some more unique flavor perks that do interesting things, I'm not feeling very creative right now.