Downy Wrinkle Releaser Spray. This product has been around for several years and we have used it successfully to help wrinkles just fall out of our clothes. Just put your clothes on a hanger, spritz with the spray, and give the clothes a few shakes, then let them hang for a few minutes while the rest of the wrinkles fall right out. We have used this product on multiple occasions with good results. However, I should note that if the clothing is really wrinkled, don't expect this to take away all ironing requirements, but for those that are travel-wrinkles or packing wrinkles, this does the job!
So what about ironing on a cruise ship? You don't want to look a mess, but the ship specifically prohibits items such as irons and steamers. There are a couple of options, depending on the ship you're on. Disney Cruise Line has self-service laundry rooms on each of their ships, and within each one is an iron and ironing board (or two) that are available for guests to use. The laundry room irons get busy beginning an hour or so before main dining as people are getting ready for dinner, but early in the morning or mid-afternoon are good times to go freshen up any clothing needed for the next few days.
The other option is to take advantage of the ship's laundry service. Most ships offer a pressing service for about half the cost of laundering. You just lay out the items you need pressed, fill out a laundry ticket and provide the items to your stateroom host and go about your day. Later the same day (or next if you give them later in the day), your clothes come back, neatly pressed and ready to go. The bill for the ironing is added to your stateroom account.