I'm not sure if I'm reading your question right, :? but when you check in to board the ship, they ask for a credit card and everything you buy while on board goes directly to your sea pass account which is actually attached to your credit card. Anytime during the cruise, you can pay off your sea pass account at the pursers desk; if not, the amount you spent will be automatically charged to your credit card.
I think you will need a credit card. You better check. I've never seen anyone use traveler's check for their sea pass account.