How to treat a stubborn cold sore on corner of mouth?

Asking for a friend, I swear.

This cold sore lasted for a few weeks in its unfortunate location at the corner of the mouth, where it seems to thrive due to continuous aggravation. Over-the-counter cold sore products didn’t seem to help. In fact, it’s been so persistent that we now call it Clancy. Clancy was temporarily bested with a combination of tea tree oil applied before bed to kill germs and dry it out, and Vaseline lip therapy ointment during the day to keep the tissue moisturized and pliant. The people rejoiced.

However, after about a week the creepy cold sore sensation is returning.

Other details: Clancy is shielded by neatly kept facial hair, and his host is a smoker.

What are your tried and true treatment methods?
Could this be something other than a cold sore?