Yes, you can pay by cash. The following is a paste from the Princess website:
"Those paying by traveler's cheques or cash will be required to leave a cash deposit with the Purser's staff at the beginning of the cruise."
Also bear in mind, that you may have to join a very long queue prior to disembarking in order to settle your final account.
Hi, we did the Baltic/Northern Europe cruise on Crown Princess in July this year. I paid for everything in cash at the pursers desk at the end of the cruise (I had taken US Dollars with me as the exchange rate is better here than on board and some Stirling which I didn't need to change), you will still need to give your credit card details at check- in to set up an on board account and you then have to settle your account the night before disembarkation. Any remaining purchases made after this are still charged to your credit card. I did not make any prior arrangements to do this, you just need to pick a good time to pay as there will be a queue
Hope you enjoy your cruise
Regards, Mike Rogers.
We always give our credit card details and on every cruise we do 7,10, 14, 21 day we always pay our bill in stages in cash and on last day b4 departure pay off the rest and buy a bottle of wine or beer from a bar and have a drink that night weve done 16 on princess and always do it the same way never had a problem.