Probably the easiest solution would be to use a Pi Zero W attached to the VNA and then connect to it remotely with your method of choice (VNC, etc.) With the Zero W you could even use an ad-hoc wifi connection on your phone or tablet while in the field. I look forward to other solutions (like the one mentioned), but if you want to get up and running with the least development time and a moderate cost then this is probably it.
Cheers,
John VA7JBE