Is there cell service in the Alps on the My Way Alpine tour? I have Verizon cell service.
Look at Verizon’s international page. I assume you will have it if you book their international plan.
Yes, you can sign up for one of Verizon's international plans. One is $10/day on the days you use it. The other is a very limited amount of mobile data per month (personally seems like a bad deal to me). Verizon has roaming partners in Europe. Your phone needs to be able to roam on GSM networks to work in Europe. Most modern smart phones can, but it wouldn't hurt to call Verizon and ask. (If the phone is old, maybe not.) You can sign up for the $10/day plan and never use it (leave the phone in airplane mode but turn on WiFi to use it at hotels) and never get charged if you never take the phone off of airplane mode.
Most Verizon phones are unlocked, too, so you would have the option to buy a SIM card in the first country you land in and probably roam without extra charges to the other countries. But you wouldn't have the use of your Verizon number for calls or texts (you'd have a European number while the Verizon SIM is out). If all you need is mobile data, though, this might be a great option.
I have used my VZW phone in Europe for the past several years including the high alpine trails. I'm always amazed that my cell service on the high mountain peaks is always 100% while at home I have spotty service driving down interstate 40 or ZERO service when I visit the Great Smoky Mountain National Park.
We always get the $70 pet month to US and have used it a lot without having any problems. They increased the amount of data last year. Then we get a SIM on my phone for local service and data so we have it all covered.
When I was in the Swiss Alps ( Berner Oberland area) there was a normal cell service. I used Verizon international plan; excellent connection. But, I haven't done the My Way Alpine tour, and can't speak for the rest.
I've found that the cell coverage in Europe is excellent in all countries, including all over Switzerland. There have only been a few cases where the coverage has been spotty. In your case, the coverage will depend on which European networks Verizon has roaming arrangements with. You should have no problems.
Do you need cell service? My trip was 4 years ago, there was wifi on the bus most of the time and in all the hotels.