Once I had realised that the specific zipping call I needed (to zip a single file, not using filtering) is also the one that works on device as well as desktop, I was able to do exactly what I wanted.
Which is to take a KML file that I have just created and zip it into a KMZ file for compact use with Google Maps/Earth.
And using a Shell() call I can invoke those programs citing the KMZ file too!