I will caveat that I have never tried this specifically, but I doubt it will work. Looking at the composition, I am very dubious that you could TIG weld it with any alloy I can think of as filler. A butt braze for a tang will be very weak.
If you have to try, I would heavily fillet the butt, and try brazing, though I would probably do a forge or oxy-fuel braze in lieu of TIG. I would grind flush and go from there. My gut says it is a bad idea, but it may work. The real problem here is having to grind down the braze to flat. If you could accept a large bead around the junction, it should be fine for most use scenarios, but hiding such a joint in your scales would be a real pain.
Also, the location of your joint will look strange as you will see your braise metal (presumably a copper or silver alloy) in a full tang construction.
If you are gonna try it, I recommend destructive testing on an offcut prior to constructing the knife.