I always travel with the American Express travelers checks and have never had a problem using them at cash in ports, but yes, you can always cash them onboard the ship, no problem.
also note that if you use Traveler's cheques your change will be in local currency. Use your credit card for large ticket purchases, cash your traveler's cheques at the Purser's desk - get just enough cash for the day, keep the rest of your cheques in the safe in your room.
I'm with Mike. I haven't used a travelers check in well over 10 years--and I travel fairly extensively with and without the aid of ships.
These days, a combination of credit cards, ATM's, and in-room safes just seems to make them superfluous.
At an ATM in Milan not long ago, I selected "English" as my preferred language for the transaction. After I swiped my card, entered my PIN and selected the amount of cash I wanted, the screen lit up: "I'm-a workin' on it!"
I still use TC's. I like knowing if they are stolen I can get them replaced. I also use them to limit my spending, if I run out, that's the end of my buying. I try not to use my credit card except for large purchases over $150 and to pay off my ship card. Sometimes, I will use the TC's at the end of the cruise to pay off my ship card and that way even that amount doesn't end up on my credit card. I just have an aversion to "buy now, pay later." And yes, my husband likes that about me...
Even though I think TC's are outdated, I applaud your strategy. Using them as a tool to stay out of debt is the best use of them I can think of.
I should have added to my post that the credit card strategy is only worthwhile if you pay off your cards in full every month. This also avoids going into debt, and is another worthwhile discipline.