Why not include them? I think it would help immersion, and the characters feel like a part of the world, instead of obvious tourists.
Don't worry, there are already playable races with flight... it's perfectly fine to include flying PC's in your game. Just have to constantly think in all three dimensions... which gets easier if you like to include flying enemies. And, flying enemies is the obvious answer to any BS "balance" arguments that might arise from giving PC's flight at level one.
Let the fishfolk fly, let the players pick flying fishfolk for their characters. Should make for an awesome campaign.
If there's gravity (i.e. if it's not like Karl Schroeder's Virga) then you need some means of recovering PCs who fall overboard/off the island/unconscious while flying. You know it's going to happen sooner or later, and the last is a problem even for natural flyers. Life belts which negate gravity, or something like gravity which acts towards the closest island or ship, or scavengers with nets, and/or helpful sky-dolphins or something.
Having flight and a swim speed should cost something in character resources, but it doesn't seem impossible to balance in this setting where the PCs will get a skyship eventually if they don't start with one.