You will find self service laundry rooms on the guest decks. There you will find irons and ironing boards, but no irons in you cabin. You may also want to pack your dress's in the plastic cleaner bags, saves on the wrinkles and I do that all the time, it really works, no ironing needed. So, give that a try.
Relax!!! You will likely get a bit lost the first day or two until you acquaint yourself with the ship, but it's not like you're going to get lost and never find your way back. You'll likely make a few wrong turns but you'll be given a little map to take with you. No, you can't take an iron, nor are there irons in the room. There are laundry rooms on the ship with irons, and you can take your clothes there to iron them. Or you can pay to have them cleaned and pressed - I think it cost my friend about $20 for 4 or 5 shirts. I ironed before I left and packed carefully and my stuff did not need any further care while I was there.
No irons in the rooms on Radiance. We ironed 1st & put in garment bags. Hung in closet as soon as we got to our room. In the morning if we needed to dress nice for the nite we got it out & hung on the door by the bathroom. I think the air was humid enough & we would open our balcony door & let in the moist air - everything looked fine - never had to get anything ironed. But if you need - you have to pay for service for ironing.
Have y'all seen these (fairly) new travel pouches (I got mine at The Container Store, but I bet travel stores have them, too) that let you pack 15 or 20 cotton collared shirts in a stack, then push the air out to create a compact package? It keeps things wrinkle-free *and* saves mega space in your bag. It also works for shorts, skirts and dresses, though not as well as for shirts.