Every phone should have an option for turning off "data roaming" under "settings" - this only means you don't get email or internet access, but your phone should still work.
Personally I still want my phone to work for emergencies while on a cruise. If you put your phone into airplane mode it becomes just a gamo console - no phone connectivity.
The answer to your question is to just turn off "data roaming."
According to this for customer support person, you should also turn off "wi-fi" but I don't buy that.