I believe there is a way to stop your phone from roaming and basically it just says you have no signal. My H did this on my phone when I was visiting him in Canada. Or like Sue said, leave your phone at home.
Right, your question... yes, I believe that would work.
Yes, airplane mode will keep you from Roaming. For the cruise, I recommend you take your phone if you have WiFi. A lot of the restaurants in ports have free WiFi while you sit and eat, because they like to cater to cruise passengers. H and I took our iPhones everywhere on our cruise, to use as cameras and to use the free WiFi :-)
On my phone, airplane mode turns off both wifi and the cellular connection, so you wouldn't be able to connect to wifi. I can, however, turn off wifi and 3g/4g separately.