Sure it will but you'll have to make a new heavy washer to match the new id and the old od. Then there's the matter of finding a new cap nut in that size. Would be simpler to wrap the taper with a copper sheet to protect it, weld it up, turn it down and put the right threads back on. Never saw a good machinist yet that didn't enjoy a little challenge.
Do you know how to remove the sliding shaft? Unlock it and pull it out till you see the pin in the tube behind the dash. Drive it out and the short shaft will come out. If the notches are worn repair them while you're at it. I would put a new ball in there while it's apart.