I haven't personally been on Island Star but all the ships that I have been on including Fred. Olsen Cruises which is quite an old ship, I have been allowed to use my straightners. Also depending on what ship you are on you might need to take adaptors.
I am booked on the Island Star on 16 June and I have asked about using straighteners on this ship on a few forums. The ship has American voltage and sockets and it seems that a lot of people have had problems with the 110v. I am also worried about this because my hair is a disaster if I can't use straighteners!!! I've used them in Amercia, they are 240v, and they have worked fine, but it seems that some people have encountered problems on this ship, in that they don't heat up. I'm taking both of my pairs with me and hoping for the best! You will definitely need an American adaptor though. If you find any more info about this I would love to know. Hope you enjoy your cruise.