While it isn't a complete wash I kept a wet washcloth in a dish on the kids table in the kitchen. Whenever I caught him with his hands in his mouth I would just call his name and say D....hands and point to the kitchen. He had to stop what he was doing and go wash and whatever he was doing while he was gone was not protected so if another child started playing with it while he was washing too bad. He was just told sorry you were busy cleaning your hands. Next time don't chew on them and you won't have to leave the room. Took awhile but it soon got to where I could just remind him with something like do you want to have to leave to wash as he was about to put them in his mouth and he would stop. It is a compulsion they do without thinking - in psychological terms it will stem from oral needs not met such as soother or bottle taken away too soon or not soon enough till it became a security habit.

At the same time unless the child is sick I don't go out of my way to have a mouthing bucket either because it becomes a fetish for the caregiver as the kids don't care and even if you miss one toy then all you are doing is for naught as it only takes one toy to spread the germs so save yourself the trouble. Seriously, I have no more illness in my daycare by relaxing my germ rules and in some cases maybe even less as they build up immunity during the inbetween times.