I take my uke down to florida a lot, and haven't had any problems. However, I have had huge problems taking papers down there. They turn into absolute mush in the humidity. So if you bring sheet music, it will start to feel a little damp after a while. My parents have to keep pretty much everything in plastic bags in the cupboard.
You know though, pianos, even though they are kept inside, that are close to the ocean feel all sticky to play, so I bet that happens with the uke too. You could end up with a little saltiness on your strings, but nothing to hard to wipe off.