Just out of curiosity, what types of injuries would keep a dragonrider from being able to fight Thread? For example, I assume a rider would need to have both hands (although maybe not all fingers), but how about legs? If a rider is missing a foot, or part of a leg, but can still be strapped onto his/her dragon, would that be fine? And, do people with missing limbs have wooden feet or legs?
And, how about hearing? If they're partially deaf, but could at least hear someone yell if Thread is about to hit them, could they fight? Or do they need perfect hearing?
It all depends on the severity of the injury and the healers report. Some riders would be forced into 'retirement' for example the loss of a limb or a serious underlying medical condition. Other might be directed to the Weyrlingstaff or Queen's wing which may be more suitable. Each case is different and treated that way.
I think it would be a case by case basis, but as far as legs, they would need them to grip their dragon during quick turns and turning in the straps to reach for firestone. As far as hearing, just being hard of hearing might be acceptable depending on the level. Missing an eye would be bad because you'd have a blind side. Missing a finger would probably be ok as long as you can catch firestone (so missing a THUMB would not be acceptable)...
So really it would be on a case by case basis, so if you have an idea, it might be good to run it by your L1 or the Council.
As far as wooden legs/feet, I'm sure some people do have them, but they wouldn't be secure enough to fight Thread.