How do I remove dried paint from ceramic tiles and the bathtub?
A straight razor blade shouldn't cause any trouble on your ceramic tile (assuming it has a smooth finish) or an enameled tub, but a fiberglass tub you're right to worry about.

Depending on the number of stains you're trying to remove you may find that heating the surface a bit by filling the tub with hot water then draining again will weaken their hold on the tub enough that you may be able to remove them with gentle scraping with a putty knife (being careful not to dig into the tub's surface).