Can I sync contacts on my devices with my wife's devices?

No. There is no way to share contacts through iCloud that will not cause everything else to be merged and shared.

One possible option is to make a shared contact list on a 3rd party email account like Gmail or hotmail, and set up that account on all devices for contacts only so they can access the contacts from there.

Also, note, Family Sharing does not share contacts.

You should consider Family Sharing; this is the best way of sharing things with family members (and avoid problematic synching issues if you use any other means, such as the big no-no of sharing your Apple ID): Set up Family Sharing - Apple Support

I stand corrected. Thank you for pointing out my bad advise.