Is there a cleansing product that effectively removes exfoliants?

I have a lot of fine hair along my jawline. I’ve never shaved it because I’m afraid it will make it thicker. Maybe that’s why, whenever I use an exfoliator, it always gets caught in the fine hairs and doesn’t come off even after washing with cleansing foam. I have to pick them off one by one or remove them with an exfoliating towel or sponge. It’s inconvenient, so I don’t really do it. With all the fine dust these days, I think we need to exfoliate frequently to help improve our skin.

Please recommend a cleansing foam that effectively removes dead skin cells during washing.