But call it something else than degradation. And Endurance should play a role in that. amirite?
EDIT: typo
Take it one notch further, and have it so that for every 100 points degraded (and eventually healed) you get a bonus to unarmed damage from your hits. (this reflects the hardening of the fists and experience)
Both are good ideas. Higher endurance should grant you lower base degradation rate. If you don't want to think of it as degradation call it injury. Every time you throw a punch you're injuring your fist to some extent. How much that injury is depends on lots of factors.
The damage bonus from lots of punchin' should have a cap at a reasonable level though, and should be a very small bonus each time. We don't want unarmed becoming obscenely strong for no reason. It was already obscene with the paralyzing palm perk.