We take travelers checks and cash them at the pursers desk the night before we get to a port. I also take a lot of $1 bills for tips - on and off the ship.
Also, we do take a credit card with us on the islands. As we are not big spenders, we've very seldom used it. BUT...before leaving home I contact my Credit Card companies...and inform them of our entire itinerary, including dates, and what we expect our purchases to be while we are traveling. This way, if we are supposed to be in St. John...we are not making purchases in California. LOL