For Texas it has to be a permanent upper limb disability. A temorary medical condition, like a broken arm or sprained wrist, does not qualify. I don't think a cyst will do it either unless it can't be removed or unless you have a very friendly doctor.

Also, the crossbow is legal for any game other than migratory birds during any firearms season or for any animals that have no closed season. Archery deer season is the only time they can't be used, except by the disabled. But they allow the draw lock device with no restrictions!!