I like this idea, some accidents are already in place. sparring and miners are very good at dying in mydraid ways (mostly the players fault in the latter) not to mention hunters being mauled by their prey, ect.
The rate of accidents and severity of the injury should increase with inexperience, and any status effects. Anybody thats thirsty, hungry, nausated from the sun, miserable or drowsy would be more prone to accidents.
Which brings up the fact that dwarves drink/eat/sleep long before they ever get thirsty/hungry/sleepy. Perhaps a personality trait related to a work ethic could cause a worker to keep working a bit dispite being tired or hungry? I can imagine an overworked butcher or carpenter accidently losing a finger or two. Or things like that Novice Mechanic installing or resetting a weapon trap, I imagine could be extremely dangerous.
Also, having accidents implimented would have pretty signficant concequences on all those unskilled migrants building your 20 story soap tower in the rain...
I'd suggest that some tasks like planting, cooking, making clothes, smoothing out floors and even most stone, glass and woodcrafting should be completely safe. Yes, you can poke yourself with a needle, cut your fingertip wittling or accidently touch a hot pan, but none of those things are bad enough to waste a doctor's time with. Rub some dirt in it and keep working.
I was going to suggest gathering plants to be perfectly safe, but some cave adapted novice herbalist stirring up a hornet's nest while messing with the bushes would be a cool thing to impliment.