You can definitely cruise on Princess without credit cards.
While you won't have express check-in, that's mostly gone anyway. Princess' regular procedure is expedited and you won't have a delay in boarding.
You will have to leave a cash deposit with the Purser in order to allow for onboard charging for your bar tab, excursions and other items. Anything not used will be returned to you.
Regarding the auto-tips, you can remove them, or adjust them, at any time. But one note: the tips are pooled. If you remove the auto-tip, *anything* you give your waiters or steward goes into the pool, even those amounts over the auto-tip amount. However, if you leave your auto-tip in place and wish to tip additionally directly to the crew member, they are allowed to keep that additional amount. So if you want to adjust the tips down, you can easily do that and keep the auto-tips in place. But if you want to tip more, and want it to go to the staff member who has directly earned it, then keep the auto-tips in place and then tip additionally in cash.
Regardless of how you settle your bill, be sure to check the itemization of charges before disembarking. I generally get my folio printed a couple times so I don't have to do it all at once the last morning or even the last night.
One other option for you. You may want to initially give a credit card for charges for ease of boarding and setting up your account (no need to visit the Purser). Then, at the end of the cruise, you may simply pay your charges by cash with nothing going to the card. Makes it a bit simpler, but you won't have any charges on a card.
