this is what I do (the order is important):
(1) under cellular data settings, make sure data roaming is off (it is always off on mine, but i always doublecheck);
(2) under cellular data settings turn OFF cellular data -- this way even if you accidentally come out of airplane mode, cellular data is still off;
(3) then I put the phone in airplane mode.
(4) turn on only wi-fi and connect to the ship wi-fi. I turn wi-fi off when I am not using it, in part to save batteries.
If you connect to the ship WiFi just to use the app and do not purchase a data package you shoudl be fine this way.
If you do purchase a data package (or get the free 50 MB one on the first day), then there are additional settings you need to use so your apps don't go trying to update themselves and suck down your data allotment in a matter of seconds.
SW