Official policy is that travel irons are not recommended to be brought on board because of safety reasons. The reason is that the most likely place to iron your clothes is the bed and an iron left on the bed is very dangerous. Fire is the worst thing that can happen on a cruise ship.
Does that mean that people don't bring one on board. No. Does that mean you should bring one on. No.
There are some great alternatives: Downy wrinkle release is a great product. Packing your garments in dry cleaning bags works wonders to reduce wrinkles and using dry cleaning bags between layers of clothing also is a great way to prevent wrinkles. The old standby of putting clothing in a steamy shower is my favorite way of eliminating wrinkles when they happen. Careful packing is the number one way of packing without wrinkles. As a last resort an onboard iron form the laundry (if available or sending it out for is always available.