The only thing I have ever been asked to show my passport for in Europe (other than airports) is checking into hotels.
Warn your credit card company that you'll be in overseas, and in several countries, so they don't stop any purchases you might want to make. I've used ATMs in Europe with no problems as well. Use bank ATMs, and don't use the sidewalk money exchanges.
Don't exchange money on the ship because their rates are way too high.