The first one that I made used one of the "pencil" type die grinders and was rated at 60,000 rpm.
Basically, I put a top collar and bottom collar on it to resemble an R8 collet that my spindle uses. Then I took a piece of 1/8" Brass pipe and threaded it externally for the putting a nut on the top of the spindle to hold the air spindle tight. This was also internally threaded to allow the pipe/drawbar to be threaded onto the top of the air spindle and also to accept air on the top end.
Worked very well.
The taper on the bottom piece was made by mounting a rod (5/8") in a collet in the mill, and then clamping the raw stock to it and using the mill like a lathe to cut the taper. A lot easier than trying to do it in the lathe.
Couple of photos that I hope helps.