Can you "Share" a Watch?
There was another post on here that said that the watch is wiped whenever you unpair it from your phone (you can repair it and restore it from a backup later) so it might be possible to unpair (and wipe) then pair to your wife's phone and have her restore her backup, then do the reverse to get it back with your phone, but I don't know how practical that would be on a regular basis. especially considering that your apple pay cards would be deactivated on each wipe and need to be reactivated each time.