Now you might say "you have a lathe, dummy! Just turn the shank down! Piece of cake!" Alas, the end mill is carbide. If I tried to cut it with even a carbide tool, I would ruin the shank, certainly the tool, and maybe even the lathe. Not an option!
The only way to do this with my equipment is with a toolpost grinder. But nobody makes one for the Taig. So I improvised one. I started with some 1/4" - 6.3 mm steel square bar from Lowe's. Nice nickel finish on it, too. The Taig toolpost takes this size. Ten second's worth of time with Handy Bandy cut it off. Then I milled the ends square.
In the end, it took a long time. The grinder does not like big cuts. Furthermore if the grinder axis is off-center you will grind a taper on the shaft. So you have to measure the shaft at root, middle, and end and adjust the toolpost accordingly. There is no way I can get a dial indictor into this setup, I sure tried enough, but no room. I practiced on a broken drill bit until I got the angles right. I wore out 3 grinding wheels in the process. Carbide is very hard. Also things tend to move. So it's grind, measure, reset, go again. Took, essentially, a full day.
But it worked. The new shaft fits, just, the 3mm collet, so I have a 4mm endmill at my disposal on Cecil B. de Mille.