You can give a bunny a butt-bath and you can clip the hair, although never ever the hair under the feet, they need that because they don’t have foot-pads. If you cut his fur you need to be very very careful not to nick his skin.
The bath-water should be lukewarm and you should pat the area dry after with s soft towel, micro-fiber is the best. You can use a hair-dryer but make sure it doesn’t get too hot for him.

I would suggest trying the butt bath first before you clip the hair. sometimes its just the dry feces holding it all together. I also wanted to know a little more about your rabbits wet butt problem. is his butt wet because his poo is still that runny or is it wet because he sits on his wet litter? If the latter is the case, may I inquire what kind of litter box you use? You can try a wire bottomed litter box. I know some people are against wire bottomed anything but if its just for the litter box it should be alright. wired bottom litter boxes are what I use for my bun.

Here are the instructions for a dry and a wet bunny butt bath from Dana Krempels:

http://www.bio.miami.edu/hare/buttbath.html

The few times when I have had to give an elderly or sick bunny a butt bath, I used the bar soap that I use for myself – Clearly Natural. It is hypoallergenic, cruelty free and comes in a few scents, plus fragrance free. I used to only find it in natural food stores, but regular grocery stores have it now.

Personally, if I wanted to shave my bunny, I would go to a vet/vet tech to get it done. Especially around the tail/butt area. I watched a vet tech shave a severely matted rabbit once, and the tail was one of the hardest parts. I imagine it is more difficult for someone who isn’t trained at restraining and clipping. Clippers can also get hot quickly, which can hurt delicate bunny skin.

As for bathing my friend and I bathed her bunny before. He also had mats and poop stuck to his bum. We put him in a shallow, lukewarm bath with water that was only high enough to soak his butt in. We tried to wash as much of the poop/mats out as possible then used some child safe scissors to clip the rest out (not cutting close to the skin). Then made sure to dry him very well (i think you can gently blowdry if your bunny is not afraid of the sound)

Butt baths are pretty easy-I run the water so it’s warm from the tap, and hold my bunny and angle the bum/dirty area under running water. I rarely use shampoo but you can use any gentle shampoo/dog shampoo. Make sure it’s rinsed, they have very fine hair so you’ll need to rinse heavily. But water is just fine and does the trick. AS you are working keep your hand massaging the fur to loosen the gross stuff AND more importantly ensure the water isn’t too hot or too chilly.

I use a few towels to press the water out, and keep an eye for 24 hours for signs of your bunny being cold. You may have to blow dry (on cool/low using your hand to again make sure it’s not too hot) or put a space heater on. It’s like you getting out of the shower and sitting in wet clothese for hours, it’s chilly so make sure they stay warm while drying.

I don’t know if this is safe for a bunny (so hopefully someone with knowledge will say one way or another), but our skunk, Elliot when he got to be about 10 years old became very incontinent due to some kidney issues. He was double coated and had a ton of hair and I didn’t like using soap on it. I would do a butt wash with vinegar and warm water in the sink Vinegar helps get out urine/poo pretty well and kills bacteria naturally so helps with the skin if it’s getting urine on it. Rinsing out vinegar is not as stressful as trying to get soap out of fur. It doesn’t have the drying effect on the skin that soaps can have.

Over the years we’ve had poopy butt issues with our layer chickens as well. We do a vinegar/warm water soak with them as well.

I’m glad you got it sorted! =)