I have two amex, one visa, and a debit card. Always wait to get overseas to hit ATM at airport. We do have bags of left over currency that we will take with us (along with transit cards (Oyster, etc)). Last thing you want anymore are travelers cheques; hard to cash.
My last cruise was a little strange. We were in Australia for a week. The ship bought back my Aussie dollars for a lot more than I paid for them. If I had realised that at the start, I would have hit ATM in every port and sold back every day.