I use a different type of smartphone. First of all you should have an app installed on your iPhone for Skype or Vonage or both. In order to call you need to connect to a WiFi connection likely provided by the hotel you’ll be staying in. Once connected open one of these apps and place your calls via the WiFi connection.
My smartphone has a Settings option where I can turn on or off both WiFi and carrier provided Internet connections. So if you want to make sure you’re not going to place the call using the carrier provided data plan look for the option to turn it off.
Not sure why you’re trying to call in Airplane mode. As far as I am aware, even if you have a subscription to an inflight WiFi plan they don’t allow calls using Voice over IP.