I would start with the least aggressive method. You can always work your way up from there.
Get hold of a rotary buffer and wool pad and try to polish it out first.
I wouldn't waste my time with a random orbital and foam pads on a boat. I have a PC 7424, and a Flex 3401 that do great things on my cars, but they don't seem to be able to do any correction beyond some light polishing on the boats.
If that doesn't work, then move to a compound and a more aggressive wool pad.
If you borrow a machine from someone, they will probably have more than one type wool pad they use with their machine and will show you which one is for compound and which is for polish. There is a difference.
If that doesn't work, then you can move up to the wet sanding. You could pass by a body shop and tell them what you are looking to do and that you are a little nervous about it. Then ask them for a couple of scraps of some 1200 or so grit that they've already used a little bit, but that still has some life to it.
After you wet sand it you can compound, then polish as I described before. That should get rid of any trace of marring that you put on the finish with the wet sanding.
It might not come out perfect, but I'll bet it winds up looking a lot better than it does now.
You shouldn't worry too much about using a rotary on your boat. Unlike your car where a novice can do real damage to the finish on a car, the Gel Coat is pretty tough and hard to mess up if you take your time with it.