'Practice', I think, is the best verb: I practice karate. But 'do' will do. I didn't know that 'judoist' was a word, and I don't think it is a very felicitious coinage, but if it is acceptable, then certainly kendoist, kyudoist and karateist are, as odd as they look.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.