I'd call 3M. For two reasons: they make all sorts of tapes, and I second the concept of using a waterproof tape and poly, since you WILL have to mask off the teak anyway. In fact, 3M makes a "blue" masking tape with poly attached to it, so you can do the masking in one shot. (Any hardware/paint store.) But they also make more durable tapes. If the tape will be left in place exposed to sunlight for more than a week, you want a more durable tape so the gum doesn't transfer to the wood.
3M also makes a full
line of painting and refinishing supplies including "prep/solve" a solvent that removes all waxes and polishes from fiberglass to prep it before painting. Yes, you can use that instead of TSP, which is banned in many states anyhow. It will cost more--but like most solvents, it shouldn't raise the grain of the teak. You could probably clean the deck with prep solv and clean rags, THEN mask the teak after it had evaporated off. (Should also clean the teak well enough to get the tape stuck down nice and tight after.)
****'n'span used to be mainly TSP, the ban made then switch formulas AFAIK.