Apple Watch LTE with a different number than iPhone

Read this to help you

https://support.apple.com/en-gb/HT209043

While it would sound feasible, if you cancel the service on the phone, then I don't believe the Watch would continue to operate. The Watch needs to have a the phone paired to it, and if you don't have that number in the phone, then I believe the pairing would fail. But that may be a question to ask Apple directly.

Apple Watch is designed to be paired to your iPhone and configured on the calling plan to share the same number. What you are planning would probably work for a short time before causing mayhem in the data transferred over Bluetooth between your phone and watch. One critical problem might be incoming calls to the new phone number which would also be forwarded to the watch, but from the wrong phone number.

Thanks for that link. I'll add it to my group of tools in the toolbox.