Dubbing ?

Rabbit fur has soft fine underfur and coarse longer guard hair.

You can get a dubbing rake and mix dubbing as you tie or you can use a sharp pair of scissors to cut the fur from the skin and put it in zip lock bags.

In either case, pull the guard hairs and take only the underfur for dry flies and include the guard hairs for coarse nymph dubbing.
If this is a harvested skin, you might want to treat it with a salt bath before you store the skin. If you cut the hair from the hyde it will not matter.