Sorry to be replying to myself, but for those interested...
It helps if you put the right words into XP's Help and Support centre search field.
You DO have to switch off internet connection sharing on the current host computer before changing hosts. Then, as
manoffewwords suggested, run the network setup wizard, first on the new host, then on the client.
Given that the network was already set up and working, I suspect you can swap client and host manually just by checking and unchecking various boxes, but for those not network savvy, the wizard avoids pain.
I discovered the hard way that ZoneAlarm must be disabled during this process because the IP addresses may change and ZA blocks the new ones. I eventually had to uninstall ZA from the new host computer and then reinstall it to get it to configure itself to the new arrangement. That only took a minute or so, but it took me ages to figure out that's what I had to do.
Now for the wireless network, for which this reconfig was preparation.
Subject to treasury constraints (Mrs AA), of course.
AA