Welcome to cruise-chat. No irons or steamers allowed onboard Regal Empress... she's a 1950s liner with beautiful wood decor, so this would present a fire hazard. Click here
and scroll down to "What to Pack?" Essentially, it's casual during the day (swimsuits, sundresses, shorts), and shirt/pants/casual skirt the first night, perhaps a button-down shirt and slacks or (for you) a simple dress on the second if you want to get a little more dressed up.