You cannot pay cash for anything. There is no cash at the bars , stores,etc.
You can leave cash at the beginning of the cruise when you check in but at
no time will anyone take your cash. Why do you have to drink so much anyway?
The casino will take your cash for gambling, but that's about it. You'll receive a receipt to sign with each and every drink. You might try being the first in your cabin to pick up your statement delivered the last night of the cruise, discretely tuck it away and then go down to settle up, inquire if you could perhaps pay partially in cash, and then put the unpaid balance on your credit card. Tuck away the original statement and receipts (or conveniently misplace them), wife receives the credit card statement in the mail showing a reasonable amount of ship's charges, and you're off the hook. ; )
You can always pay down your onboard bill with cash during the cruise. I've seen people at the purser's desk doing that. This way, the final bill will not be as much ... though all the charges, and the credits where you paid down the balance, will appear on there.