Hi miffymoo
When I volunteered at an L.A. city shelter in the bunny room, i was the bunny groomer. I had a HairBuster, a ZoomGroom (see end of post)
a li'le pals puppy comb, scissor-type nail clippers, q-tips for scent glands,
and a small pair of good quality scissors made for trimming infant fingernails. They have rounded tips and altho quite sharp they are easy to control. Frequently I had to trim
genital areas down to the skin, and a few times I had to give full body fur cuts because of unwashable dirt. It was time consumming but there was no other way to get the body so that the bunny could take care of himself by himself. I'm proud to say with three full-body cuts I made only one small nick that healed within three days. And a brown bunny grew in white. The scissors are specialized but not expensive.
In the face of severe mats and delicate bunny skin, I think one must carefully cut off the matted parts. Follow up by gentle combing often enough to keep more mats from forming.
A ZoomGroom is a grooming tool made by the same company that makes the Kong dog toys. There's a zmgrm for dogs and the same smaller for cats. It's the only tool I recommend for children to use with bunnies. It's very gentle and works by creating drag through the fur. I have found that a petting motion with it is soothing to bunny but useless for removing fur. I did see another volunteer use kind of a scrubbing circular motion and that did help a shed, but I've never perfected that. More than a few volunteers have tried other brands' knockoffs, and they have proven worthless. So look for the Kong name.
I hope this helps.