We take along a small, folding travel iron that weighs just a few ounces. (The handle folds down flat)
We asked on our first cruise and were cautioned about the fire hazard and told not to leave plugged in. It was always stowed away when not in use.
For the most part, you can hang your clothes in the bathroom while you shower and the steam will remove most of the wrinkles. Also try to take things that don't wrinkle badly and unpack and hang clothes immediately on arrival. Following this, in a 14 day cruise, I think we used the iron two times at most.