Something is wrong if a bun’s butt is wet after he pees. Wet fur will harm the skin and can cause urine scald and/or offer an ideal environment for skin fungus or bacteria. I’m pretty sure you know all this, so I’m only mentioning it, it could be helpful for other readers of this thread.
You can give a butt bath, and you can give him a sanitary shave. A vet tech can do a shave and show you how, so you can maintain the fur short. It’s a bit difficult to do it yourself, since rabbit skin is so delicate. Once the shave is done, you can put barrier creme (diaper rash cream, vaseline, bees wax salve etc) on the skin, to protect it from moisture.
A not uncommon root cause of incontinence in rabbits where the symptoms dont fit a UTI, is e cuniculi infection. E cuniculi is an intracellular parasite that many buns carry asymptomatically. They can suddenly start to show symptoms, and iys not fully understood why. Ec typically affects the central nervous system and/or the kidneys. It is treatable with fenbendazole (Panacur) for 28 days.