I am a fair skinned red head and I have seen the boat plenty of times in the harbour down here in Antigua. I would say that I would feel comfortable on the deck of the ship, there are plenty of places to "hide" from the sun and still have fun. The sails are HUGE and I am sure that they have places to go while you enjoy your drinks on deck.
Hope this helps!
I hope to see you in Antigua soon! Cheers!
The sails on the Polynesia's four masts provide plenty of shade when they are raised. However, when sailing, you may have to move around a bit to follow the shade. There are plenty of other places on the ship to get out of the sun. When at anchor or docked, the sails will be down.
Also keep in mind that when the ship is underway and you have the cool ocean breeze, you may not notice the heat of the sun and will burn very easily. Bring plenty of sunblock and use caution - especially on the first couple days - or the resulting burn could really put a damper on your trip.