Later in the service life of the Iowa class battleships, they carried UAV's.
Furthermore, it is highly unlikely the missiles would be able to penetrate the armour. Remember that the Iowa class battleships were designed in the age of dodging hundreds of heavy naval shells, heavy armour piercing aircraft bombs, and many torpedoes. Remember that the much less armoured German battleship Bismark was still afloat and was scuttled by its own crew even though the Bismark took a terrible pounding, but remained afloat, and the interior remained undamaged. The Iowa class battleships is built to take severe punishment. Ships built after the Korean War tend to be built much less lightly, and place more of a emphasis on intercepting the threat, rather than being able to absorb damage. At most, you would give a Iowa class battleship a very bloody nose, but it would still be able to steam away.
It is not particularly true that the Bismark is less armored than the Iowas, the Bismark is designed to fight in the north Atlantic where with the heavy seas, the fight will mainly against the horizontal projectile. hence, the Bismark belt is 320 mm thick where the Iowa's is 305mm (12") thick. We also have to consider the quality of the armor, which in some estimates is 5% better than USN ones, while if we look at tanks, up to 30% better.
This close in nature of the Atlantic is also represented by the Bismark's guns which fires at a higher velocity at a flatter trajectory.
I will think that a modern anti ship cruise missile will likely sink the Iowa. the Vittorio Veneto with superior deck armour and weaker main belt than the Iowas were sunk by the Fritz-X of only a 320 kg warhead at 770 MPH compared to a SSN-22 Moskit with a 300 kg warhead at 1750 MPH. now if we talk multiples....