You should never give rabbits baths, so he is rightfully terrified of them. No rabbits should get baths, unless for medical purposes, and even in those cases, it is not a “bath” but a shallow water pan of some sort in small target areas.

Your rabbit will do a good job cleaning up the stains himself, so you don’t need to worry! If you do feel compelled, a damp towel and dry towel will help. If they are getting consistently stained, I would actually spend efforts on making sure his litter boxes are clean. Perhaps you need to clean them more often if he is getting stained so frequently. Alternatively, it might you need more absorbent litter so the pee seeps in quicker, rather than being left on his paws.