You can cash traveller's cheques at the Front Office, however you cannot "pay as you go". When you board you will get a sail & sign card. Everything you purchase, in the bars and shops, & Spa, will be charged to this card. You can use cash to buy chips in the Casino & BINGO cards. When you board you will be asked to go to the Front Office and give them a charge card - VISA, American Express, whatever, - they will make an imprint and then the morning of the day before you disembark you will receive a preliminary bill under your cabin door.
What we started doing was paying off this prelim bill sometime during the last day with Traveller's Cheques and then anything we bought that last day was put through on the VISA. We did this because we are Canadians and the exchange rate is quite high - we didn't want to get a shock when our VISA bill came in.
Hope I have made myself clear - if not, ask again.
You are going on a beautiful ship - ENJOY!