Hmm... dislocated fingers look really nasty but would be an easier fix, then?
A soldier with one arm is only half as good a fighter, if you take the pain out of the matter. Considering how most people (drunk or not) would be completely incapacitated by having their arm mangled, this is a fundamental testament to their value. A missing arm isn't the worst injury one could be starting a dungeon with. I've had to deal with worse ones in my tabletop gaming experiences.
Attempting to fill out one's party with tavern-dwellers isn't a particularly good idea, either. Many key fantasy dungeon-crawler elements are predicated on phenomenally poor ideas. A crippled drunken ex-soldier is par for the course, really.