WhatsApp is linked to the phone on which is installed and, obviously that phone's number.
After installation on the phone, it can be installed on a Mac; but it only works though the phone and its number. It cannot work independent of the phone.
See it this way if you like: the phone acts as a conduit to the Mac. It is to and from the phone that the messages are sent/received; and from the phone passed to the Mac or received from the Mac.
So, if you use your Wife's phone (and its number obviously), it is to and from her phone that all messages will be sent and received - then conveyed to/from your Mac.
NB. If I've read your statement above correctly:
I absolutely don't want a situation whereby I am somehow eavesdropping on her Whatsapp messages; and vice versa.
;
it implies that your wife already has WhatsApp on her phone. I cannot imagine a situation - meaning I think it's impossible - to have 2 WhatsApps on her phone, effectively linked to the same number.
Ian