You can take a small iron on board but where oh where will you do your actual ironing? In a standard cabin you have a choice of the room desk (with towel on top) or the bed. Not the most comfortable of choices. Plus those travel irons never seem up to the task of ironing more than a handkerchief! Here's what I do. I choose evening wear that's packable and resists wrinkles. Keeping the garment in its dry cleaner bag or even one of those store vynl bags seems to work pretty well. On arrival, I unpack evening items first, give them a good shake, hang them on the back of the shower door (one at a time) and let them have a steam bath. The steam from the shower does a pretty good job but you might have to steam more than once. This method worked great on a trip I took to Italy where the bathrooms were blessed with hot, hot water. And if those methods fail, your cabin steward is there to rescue you.
FYI -- Hotels and ships don't like room irons because some folks are not careful about placing the iron in a safe, fire-resistatnt spot when they are finished.