Hi
If your Apple Watch is not yet unpaired, then follow the instructions here (under "Erase your Apple Watch") to erase it manually:
Unpair your Apple Watch and iPhone - Apple Support
Activation Lock (which prevents unauthorised use of Apple Watch if it is lost or stolen) may also be enabled:
About Activation Lock on your Apple Watch - Apple Support
If so:
After erasing the Apple Watch manually, your wife's iPhone will prompt you to enter your Apple ID and password upon starting to pair the Apple Watch to her iPhone (via the Watch app):
Enter your Apple ID and password on her iPhone when prompted:
- This will remove Activation Lock and enable her to continue with pairing the Apple Watch.
- Your credentials will not be saved on your wife's iPhone.