Yes, fragrance free gentle shampoo, especially the kind made for babies or sensitive skin adults, will be fine. You actually don’t want to bathe bunny much. Do not ever wet his head, face and ears. You can hold him and dip him into just 2-3 inches of water in a tub, sink or plastic dish pan. Make the water warm, and wiping his back end with a washcloth with the shampoo or mild, unscented soap will scrub it off without total submerging. If he is too wiggly, just stand him in it (again, only 2-3 inches), hold him firmly and wash by slipping your hand or the washcloth underneath him until the mattes and dirt come free. Keep water warm but never hot or cold.
Have a nice big towel ready to wrap him in to dry off. A blow dryer isn’t really necessary because if you towel dry him, then let him back in his cage in a warm room, he will lick himself and air dry. If he’s really soaked, the dryer should only be on low, mild heat and several inches from him.

Will he let you snip them? Wooly doesn’t like being brushed down there, but he will hold surprisingly still for me if I snip the little mats off. You just have to be careful. Don’t pull the skin away from the body because you could accidentally cut it. Also watch out for that little tail.

Ringo gets matted hair quite a lot under his tail, I try and pull it off gently and trim it, but he hates it! When he went for his last check up the vet just gave his bum a little shave with some hair trimmers and it was all gone.