1990 sport nautique non skid foam

I've read that mineral spirits will not harm your gelcoat. I have done this in the past but use at your own risk...

I would use a heat gun and lightly heat the areas and peel the old non skid off.

Take a paper towel or rag and lightly cover in mineral spirits. Lay the rag on the area and let soak for a few minutes. Then scrape off the residue with a plastic scraper or putty knife

Clean area with isopropyl before applying the new non skid.