There are small stand alone BBQ units that use a propane bottle and legs that fold down. I was never comfortable with using them, and they wouldn't last long if stored on the boat, but they are cheap. If you could find a fire resistant mat to place it on that would be good. While we think of anchorages as being calm there are jet skis, water skiers and just plain A-Holes who will give you a wake while you're cooking. I've always liked my rail mounted Magma, which is now 20 years old (And has had all internal parts replaced.) Rail mounted pretty much stay put - which is a good thing. And It's my observation that these units are most hot when the propane bottle is new and as it is used become less hot. The temp control is somewhat adjustable. Add wind and it's a crap shoot.
And there are plenty of folks using portable charcoal grills, so ....
You may find a used Magna but it's likely you'll end up replacing components which will shortly make it less of a bargain than you thought. One year I overwintered a batch of hot dogs on the Magma. Do you really want a used one?