You're making some iffy assumptions about your Note 4's capabilities for online connectivity. Your Note 4 has two wireless types to get online access -- one is cellular and that's dependent on your cellular service (currently Verizon); the other is WiFi and that's dependent on a WiFi signal based on your broadband connection with an ISP. A cellular signal will have an effective range measured in miles while a WiFi signal is much, much less typically under a few hundred feet. A T-Mobile hotspot is going to give you a WiFi signal, that instead of using an ISP is sourced from T-Mobile's cellular service so that'll be fine for online access in general and as long as you can get buy with WiFi Calling only it's no problem. If the T-Mobile hotspot is battery operated, you might want to get an external battery too. If it requires a 120v AC however, you then have to be really attentive to where you go and still be able to use your phone so you there's always a power outlet available. If you want to keep the same phone number that you're using with your Verizon service, transferring a phone number from carrier to carrier is typically a seamless issue. But in your scenario restricted to only WiFi Calling, be sure to make it really clear to the T-Mobile person you're in contact with about the changeover that it's not just a matter of switching carriers and keeping your same phone number, that WiFi Calling only issue could be a problem if your particular Note 4 model won't fully support carrier-based WiFi Calling on T-Mobile's service. You might want to get a free Google Voice phone number and just use that for WiFi Calling. It's not tied to any carrier as all it needs is some kind of online connectivity. (But as a caveat, it is Google service and like all Google apps will be deeply integrated into your overall Google account. In some ways that's really convenient, in some ways its just another source for Google data mining.)
What model of Note 4 do you have? It should be something like SM-N108V. If it is a carrier-locked model to Verizon, it might not be just a matter where Verizon needs to unlock it. Every carrier relies upon their own cellular network, and they each use selective frequency bands that occasionally overlap each other but are mostly are isolated from each other. So a Note 4 is of course a different model than a Note 5 but there dozens and dozens of variations with each. The cellular radio chip inside your Note 4 is compatible with all the bands that Verizon uses for its cellular service, but that same cellular radio chip might not support T-Mobiles bands. If you go to the link below, there are tables showing what carriers are using which bands, and frequencies. There's some overlap with Verizon and T-Mobile but read through the summaries because there are primary bands and secondary bands, and that's where they differ a lot more.
https://www.phonearena.com/news/Che...on-T-Mobile-and-Sprint-use-in-the-USA_id77933
Basically, you're likely to be going through a lot of extra effort to get that Note 4 working on T-Mobile's service. It's a seven year old model that's is also likely to be running a dated, unsupported version of Android. Might be time to just retire it as a local usage only media player or something like that, and just buy a newer, more capable phone as a daily usage phone.
https://www.gsmarena.com/samsung_galaxy_note_4-6434.php