Gfci or rewire.

If you put in a gfci I'd connec the ground to the metal box - wood is not a great ground but with the gfci doing safety purposes wood is enough for some things that want ground (that is a shield). If you can get a ground wire to enough places connected to enough different points it will fool most ground testers - remember that this is only useful if a gfci is providing safety and your goal is to fool the other reasons you want a ground.