Thank you everybody who replied.
I ended up using the same AP on my phone as I was already using for the WS-2000, so they were connected to the same network over the same WiFi router. Just saying.
Then, it took several attempts, AWNET showed the the correct MAC, v4.0.2, and available v4.0.9 update, frequently timing out, but eventually, the WS-2000 appeared to be updating, though it took a power cycle and reboot for it to be evidenced in the About screen on the WS-2000.
Kind regards,
Kelly