I don’t think you quite understand Wi-Fi Calling. First, it works only over Wi-Fi; it does not work over cellular data. So it is irrelevant if you have a data-only SIM or not. If you are not connected to Wi-Fi then Wi-Fi calling will not work.
Second, it does not require an app. It is a feature of your phone, and must be enabled (provisioned in telco language) on your account. And once enabled it should be left on all the time, whether you are home or out of the country.
It doesn’t matter where you are; as long as you have a Wi-Fi connection (such as in your hotel, a cafe with Wi-Fi available, a MacDonalds…) you can make regular calls over Wi-Fi and it will be the same as at home. Your number will be the same, you can call a number in your home country on your unlimited plan. If you make an international call using Wi-Fi calling you will be charged the same thing for that call as if you were calling from home.
Verizon has a pretty good roaming plan; I think it is flat $10 a day for any day where you use it. Considering what the travel will cost, that is a drop in the bucket.
