i had a couple of tubes of "cork grease" left over from the days i used to repair musical instruments. used them on the corks grips of my rods,softened them up & made them pliable again ...
it is used on clairnets to keep the joint tight , no problems with it on the rods . you can get it at any music store , comes in a tube like chapstick
. we also used to use vaseline on new cork , just had to wipe it down good after it soaked it to get rid of the greasies ...
derf