You can use cash/travelers checks to make your sail/sign card sort of a "debit card". The exact amount of the deposit [which, depending on cruise length ranges from $100-$350] required for your cruise can be found on the CCL site. Also, it might be in the booklet you received with your docs/or the brochure.
The do not care how your account is covered, just that it is. Cash, TC's, debt cards or CC's are all good. What many do is get a CC that they use only for cruises and pay it off as soon as they get back from the cruise as that keeps a nice record of your expenditures and even builds credit. It they have a large interest rate it does not matter as you pay it totally off immediately so you have no finance charges, just make sure you do.
You can deposit CASH, when you spend all of it on your S&S card they will let you know.... I used our Debit card last year & worked OK..... You get your bill under your cabin door the last night at sea..... I plan on using a second debit card just for this upcoming cruise since I have most of our income in our primary account..... Just a note..... My wife wanted to buy some sewing cloth in the Grand Caymans at a little shop off the beaten path, It was going to cost me twice as much using cash so I used my debit card at 1/2 the cost... I was nervous over this transaction, it took over a month to clear my bank...... A debit card with a smaller balance would be safer to use..... hope this helps...