Much ado about nothing.
Carry a driver's license or some other sort of government ID (like you do every day of your life) along with your cruise card and you'll be fine. Leave the bloody passport in the safe and stick a scan of the data page in your wallet like Kuki says.
This works pretty much all over the world. I seldom carry my passport whether I'm cruising or doing land travel except when crossing frontiers (unless the hotel doesn't have a safe--rare these days). I've never carried a passport around in Eastern Europe, Western Europe, Egypt, Jordan, Japan or even China. The only place I've really had to do it was Russia and that was because they wanted to stamp it after we got off the ship.
This is simply not a big deal. You need to have a passport, but you don't need it with you every minute. Once upon a time you needed it to cash travelers checks and stuff like that, but nobody even knows what travelers checks are any more, so that's off the table.
Just relax and have fun.