First of all, don't use essential oregano oil to pull with! Essential oils are harsh and could be harmful to put in your mouth. Use oil of oregano only!
And yes I shop for oregano oil that doesn't use an olive oil base. In liquid form I use OO (Olive-Oil) by NOW (good price and effective). I've also used oil of oregano capsules that had a base of distilled water and lethicin instead of olive oil. Can't remember the brand but just check the ingredients while you're shopping.