Not a good idea.
The Cellular + GPS Apple Watch has a built in eSIM which is used to share the iPhone's phone number, and the carriers that support the Apple Watch charge a monthly fee. In the U.S. the fee is $10 per month. Here is a list of carriers that support the Apple Watch:
https://www.apple.com/watch/cellular
So you would get your Wife's iPhone phone number, and your Apple Watch would get your Wife's phone calls, messages, email, contacts, etc...
If your iPhone supports Dual SIMs, you could get a 2nd personal cellular plan on your iPhone, and pair your Apple Watch to the personal cellular plan.
Use Dual SIM with Apple Watch GPS + Cellular models
https://support.apple.com/en-us/HT209043
Use Dual SIM iPhone with Apple Watch cellular models
https://support.apple.com/guide/watch/use-apple-watch-with-dual-sim-iphone-apd641d0e7f1/watchos
You can use Apple Watch Family plan and treat your Apple Watch as if it belongs to a dependent child, which gets its own phone line, but your Wife is in charge of your Apple Watch, and because it is considered a dependent child's Apple Watch, it has limited capabilities, as the dependent child should not have access to iPhone features that a normal iPhone/Apple Watch pairing enjoys.
Apple extends the Apple Watch experience to the entire family
https://www.apple.com/newsroom/2020/09/apple-extends-the-apple-watch-experience-to-the-entire-family/
Set up an Apple Watch for a family member
https://support.apple.com/en-us/HT211768