Allow sheep to eat mycelium

My family currently has a home base on a mushroom island. We have brought sheep over on boats, but I had to silk touch some grass into their pen or they never regrow their wool. I'm the sort of person who greatly dislikes changing the look of a biome, so I don't really like that. It would be cool if sheep that eat mycelium looked different from normal sheep, similar to mooshrooms, and had some different shearing drops (such as mushroom blocks, mushrooms, etc), but it would be fine if it were just a normal sheep and only cows are susceptible to fungal takeover. Just let the poor creature eat blocks other than grass.