I have an extra v1 lamp socket and was wondering if it works with the Wyze Cam v4.
Welcome to the Forum, @KurtK! 
Yes, and the Help Center is your friend. You should see this available if you navigate in Cam v4’s Settings ➜ Accessories. (Maybe you don’t yet have a Cam v4 and that’s why you’re asking, so you wouldn’t yet be able to see this.)
See also this Lamp Socket Help Center article and product page.