Technically, you might be able to do at least the keyboard part of it using half of one keyboard each, binding keys on your half in your installation of wow and unbinding everything else, and vice versa.
Or one of you could be using an X-Keys Pro of some kind and the other the normal keyboard, just bind all the x-keys keys to ctrl-shift variations of all the keys or something, and keybind accordingly.

But either way, one of you would be without a mouse.

A lot cheaper and easier to get a new computer of some kind.