If the USB plug is just a plug and doesn't have any electronics of its own inside, you should be able to use a multimeter to find out which wire corresponds to which pin in the plug.
You could either buy a new plug to solder on to the ends of the wire, or find an existing keyboard cable with a similar plug (e.g. the one you illustrated, unless you need that in a different keyboard) and sacrifice it - snip the plug off the end with enough wire to comfortably solder the ends of the wires together.
I did something similar for a Model M I was resurrecting, although that was PS/2 and fairly well documented.