How to clean a fuzzy plush toy that plays music?

My son got a little plush bunny that plays music from one of my coworkers. When she gave it to me, it was already used so it was a little dirty but it was fine. Now, it's starting to get a little gross and matted after being chewed on, dropped on the ground, etc. I can't seem to get it clean at all just using soap and a washcloth, but can't put it in the washer because I don't want to break it and make it not play music anymore. Any suggestions?