Non-Kosher Toothpaste

If someone was given special toothpaste to leave on the teeth for 30 minutes after brushing or too sleep with the toothpaste on the teeth, Is this a problem if it doesn’t have a hechsher since it may be swallowed, while it is being absorbed into the teeth?

The toothpaste is considered inedible, and does not need a hechsher. For further clarification see

All the best
Rabbi Shay Tahan