Well, if we raze all offshore cities, that'll leave a lot of empty space. Which means that we're going to have to keep going back and clearing out newly founded AI cities.
I don't know for sure how helis work, but I suspect they're like other air units, which would mean that we'd need either a city or an airfield for them to operate from. Does anybody know how airfields in neutral territory work? Can we use them? If so, can the AI use them? Can they be pillaged by the raging barbs that'll pop up in all the empty space?
If nothing else, I strongly recommend keeping at least one city per island, so we have a foothold. And I'm not sure I see the drawbacks to keeping more - it'll give us more unit support and some specialists, at least.