I also agree that a cleaner wax is the best try here, simple, cheap, easy to use, available everywhere. Regarding your second sentence, not necessarily; Discoloration and contamination can quite probably be just at the surface, in fact that is usually the case if the paint has decent coating thickness. If very deep or oxidized, it might need wetsanding with super-ultra-fine sandpaper or polishing "compound"; Meguires (IIRC) used to make various grit polishing compounds suspended in water in convenient squeeze bottles, I used it on lacquer after fine felt-block sanding to remove orange peel, to do a finish mirror-polish with a buffer and shearling wheel. (Geez, 40+ years ago.) But quite often, a cleaner wax will refresh things quite nicely.