You don't really have to remove the plan from the Watch app on your iPhone but it is strongly suggested that you complete the process.
Launch Watch app, scroll down to Cellular, Tap Cellular, Tap "Information" icon on the right side of where your Verizon plan is listed. Click "Remove Verizon Plan". As a final step, you should do a hard reset of your watch or simply restart your watch.
Hard Reset: Press Crown and Side button to perform a hard reset of your watch
Simple Restart: Hold side button until Options come up to Power Off.
Dave