The wire from the wifi antennas is shielded coaxial wire. You can use it as instead of a ground twist if you prefer, but it can be tricky to strip and there's a limited amount in each Wii unless you buy a small reel of it.
Note: Don't use that shielded wire for USB. USB is a differential data pair and must have D+ and D- twisted tightly together so that both lines experience identical interference. If one line gets even a little bit more than another, it breaks the world.