Yes, you can go to the Purser's desk and apply traveller's checks to you final bill. I suggest doing that the morning of the last full day because by the evening, the lines get long with people checking/disputing charges.
You can use them to put a deposit on your Seapass card OR you can just use a credit card to secure your account and then pay with the cheques on the last day. Your card will only be charged the final total on the last day. This method is easiest as then you do not have to worry about how much money to put on your Seapass account up front. Just track your spending and put awawy enough cash to pay it off at the end and you won't have a credit card charge at all.
Tink and Spiritfilled-We usually start our accounts with a credit card and monitor the balances every other day with the Purser. During the cruise we apply periodic cash or traveler's checks to reduce the final balance. We have caught several charges not our own over the years and eliminated last minute negotiations (and crowds). The Purser's are always exceptionally accomodating until the last morning!
Tink-As Spritfilled has already responded-Yes, you can pay off or paydown your cruise tab with the Purser's office at any time in your cruise. It sure helps keeping that final bill down to a mangeable size! I like to keep a handle on the bill and I don't worry about it the last night on the last morning of the cruise!
I do as Billy stated.. pay down the bill through out the cruise.
BUT, if you are only checking the charges, I know on CCL (and probably the other lines as well) you can check your charges on the TV monitor in your cabin. We use this to make sure there are not any incorrect or unexpected charges happening. A quick glance once a day is much more managable then sitting down with all your receipts on the last night. It also helps with the memory - "Did I have 2 or 3 drinks at the casino on Monday night?"