an HP printer hardwired to one of the W7s
Connected how? USB or traditional printer port?
I don't have much experience with such things, but as you say, it
should be possible to do what you want using workgroup stuff -- that's how things used to be done in the early days before networked printers.
HOWEVER, my impression is that going the workgroup route or otherwise trying to print from one computer
through another, is bound to be frustrating and flakey.
What i would do if i were in your place is EITHER buy a new network-capable printer. Whether that's a printer that can use wi-fi or one that connects directly to your router via ethernet, same deal.
That way the printer is a first class part of your network that all computers can see.
Actually however, that reminds me that i think if your printer is a USB printer, you can probably buy a router with usb printer support that would also make your printer a first class citizen in your network. So you might be able to buy a new router instead of a new printer -- choose the one that is oldest/cheapest.