Have you tried equipping a weapon in your resto-hand and then unequipping that? Should leave you with an empty hand.
Doing this during the brawl fails the quest and the guards come. However, I did this prior to the brawl to to set my right hand up in unarmed status (only way I figured out how).
My scrawny unarmoured Altmer healer has beaten the hell out of a whole bunch of tough armoured Nords and Orcs. Now I am in no way a good 'twitch' gamer, so I can't see why you would need to heal, unless you are on Master. Or is it harder than that, and I accidently did something right without realising?
Master Mode.
One word: Potions.

Nah. I used to use potions during those fights. It takes way tooooo many of them and interrupts the flow of the fight.
Just enchant you some gloves with + Unarmed and beat them to shreds without healing.
Great idea. Maybe I"ll make some for the very few moments we need them in this game.