If I got a critter that is a real mess I usually rinse them and let the dry enough to skin. I have and old clothes drier I throw them in after skinning and tumble them with a bucket of sawdust. That usually cleans them up pretty good. I do this mostly with coon, but I've tumbled rats and coyotes too. If your going to tumble something that don't need a big rinse. You still have to comb out burs and big mud balls. I tried tumbling rats once without skinning them first. Big mistake as their teeth and claw cut the hides up. Only did that once.
Mac