I have heard of wipes, but I honestly have never had to use them, so I'll check around for you regarding how well they work or if there is anything negative to watch for. Maybe what you could do in the meantime is wet a brush/comb and see if that can help clean your bunny.
Most of my bunnies haven't had to have full baths. Usually just a body part bath.
Bailey needs a regular "bum" wash because she has a crooked spine (either it's how she was made, or she had an injury before I adopted her) So she can't get to her backside so easily.
I use a shampoo that the vet gave me. Chlorhexiderm. It has an anti bacteria that Bailey needs so so I can fight off any infection due to her not being able to clean herself so well.
I don't give her a full bath, but instead clean only the areas that need it. So for example, her foot and her bum. I'll put those under luke warm running water, suds them up, and then rinse thoroughly. I really try to avoid the more dense fur on her back because it takes forever to dry.
Then I dry with cloth and paper towels (they seem to really soak up the moisture.
Sometimes Jack can get smelly, and it usually means he needs his anal glands cleaned out. eeewwww!
Other than that I just comb out the loose hair (Jack HATES to be brushed, but sometimes I do have to force the issue especially when he's molting.