To remove some of the scratches means an abrasive compound and a buffer. Your arms will not get that done. If you want a cursory clean and shine, any of the marine based products are good to use on gelcoat. I like 3M products because I've used them for years and know what they do.
I have a couple of cheap car buffers, a 10" and a 5". I don't think it takes me any longer to use a buffer to burnish a coat of wax than to wipe off by hand. You might find using a buffer is as easy as the hand work. A buffer will also allow you to rub out the scratches. Good luck with the polishing.
BTW, if you haven't thoroughly cleaned the gelcoat for awhile, cleaning the surface with a TSP addition to the cleaner will remove any oxidation.