Eliminating Thick Glue Lines in Cork

1. I use and recommend TiteBond II wood glue for glue-up.  Under pressure (thus thin…more below), it is soft/flexible enough that it turns at roughly the same rate as cork, so the glue lines never become ridges which can be seen or felt in the hand the way some epoxies can create unpleasantly eye-catching, textural ridges.  It’s a also a good color match for natural cork when used as-is.  Finally, you can pigment it to get intentionally color toned glue lines, which can really look sharp.
2. Pressure is the key.  So long as you apply TB-II to both sides of each cork ring (except the end rings, obviously), and spin them against each other which helps to fill any end-grain lacunae, thus ensuring that there is zero chance of partial ‘starvation’ at the joint, you can apply a LOT of pressure to cork when gluing.  I’d aim for at least a 1/8” reduction in grip length when under pressure, i.e., a 6-1/2” cork cylinder with 13 rings should measure 6-3/8” or even 6-1/4” under pressure….at the tighter end, the cork may not fully bounce back to 6-1/2” when unclamped if left fully pressed overnight, but you can do two hours at max pressure, then two hours at reduced pressure, then back off to just a hair tighter than 6-1/2” overnight.  This will create essentially invisible, but still strong, glue joints while barely impacting the overall length of the cork cylinder from which you’ll turn your grip.  To make initial sanding easier, I always “mop up” the squeeze-out with a paper towel dampened in warm water; also, if you’re using a cork clamp that relies on a central threaded rod, it’s good to coat that threaded rod with petroleum jelly (very, very light; just enough to get in the threads) which prevents the cork from bonding to the cork press.