Giving my Apple Watch to my wife, need help.

From the article below.

If you can't access your iPhone or Apple Watch, or if your Apple Watch isn't paired with your iPhone and you need to turn off Activation Lock:

1. On a computer, go to iCloud.com and sign in with your Apple ID. 
2. Go to Find My iPhone.
3. Select All Devices, then click your Apple Watch.
4. Click Erase Apple Watch. Select Next until the device is erased.
5. Click the remove button  next to your Apple Watch.

About Activation Lock on your Apple Watch - Apple Support

To remove the activation lock, see: Turn off Activation Lock https://support.apple.com/en-us/HT201441

If you can't turn the activation lock off and want to make it functional, you'll need to contact Apple support and have your purchase receipt with the watch serial number on it. See these support options:

Get a call from Apple support to help solve your problem using this link https://getsupport.apple.com/?caller=kbase&PGF=PGF63005&category_id=SC0245&symptom_id=23362

Apple ID Support https://support.apple.com/apple-id

Apple ID account security for country-specific and region-specific help https://support.apple.com/en-us/HT204169

Get Support: We’re here to help  https://getsupport.apple.com/. Go through the options to find the best support option.

Apple Support- What to do before you sell, give away, or trade in your Apple Watch, or buy one from someone else

Removing it from the device list won't remove the Activation Lock.