Yes, cordovan can be processed in different thicknesses, just as cowhide can be. Cordovan is better because it's from only a small area on a horses flank and is processed over many weeks to get those "cordovan" qualities. It is slick, practically waterproof, and expensive.
Having said that, I don't see why the cordovan would be rubbing your lip raw, unless it has to do with the cordovan being slicker causing your fingers to release more suddenly. I wouldn't give up on cordovan. I've tried a lot of different things, but cordovan is what I shoot.