I doubt it's unknown for carcinogenic substances to affect skin or mucus membranes they are in contact with. It's certainly not unthinkable. I know I've heard

I doubt it's unknown for carcinogenic substances to affect skin or mucus membranes they are in contact with. It's certainly not unthinkable. I know I've heard the phrases "mouth cancer" and "skin cancer". The former probably in connection with chewing tobacco. I genuinely don't know the answer to whether mouthwash could be harmful, assuming one doesn't swallow. But I've thought of the question before.