Thing with clay is (from what I remember taking pottery in high school), when it is dry (not kiln dried but leather hard), it becomes dangerous to inhale in powdered form, which, if a chin chews it, you bet there will be a powder. Also, if not dried properly in a kiln, it can go back to its original state when wet, which is dangerous to ingest. Probably not a good idea either. Those dust baths are finished with a high gloss finish once kiln dried. Any pottery that was not made especially for consumption use (mugs, or dishes are for consumption) most likely has a toxic paint base to it, as it wasn't meant to be in someone or something’s mouth. Those clay dusters are fine to have. I think if a chin wanted to eat it, it would quickly give up. Though, if it breaks or chips, I would take it out immediately.
I would just stick with wood or if you can find pumice then go with that. Or just see if Chins on the Rocks can custom make one for you?