I had the equivalent of an exercise base from another supplier, and I used either blue lace tape or vapon no-tape (which is a hard bond) when I went scuba diving. The poly on an exercise base is a lot thicker than a skin unit and you can use the really strong stuff on them without much fear of tearing the piece.

For what it's worth, I now use blue lace tape on my all lace units and have been diving many times with that combination. No problems of any kind. Blue tape is strong stuff, and it will stand up to almost anything for quite a while unless you have a really unusual body chemistry that breaks it down fast. Keep in mind that I'm not looking for the best appearance possible when engaging in water sports. I'm looking for something that will stop the unit from blowing off or floating away. That's done the trick for me for several years.