Machining Ball Screws

I am about to start working proper on a CNC coil winding project I
have had in mind for a while now. I recently discovered that
McMaster-Carr do nice ball screws that they sell by the inch. This
seems perfect as I need only a very small length.

One question I have concerns machining the ballscrew ends, one for
the stepper and one for the support bearing. I have a flexible
coupler for the stepper motor end but will need to reduce the
diameter of the lead screw. What is the best way to hold the lead
screw in the lathe while it is being turned down. I assume it
shouldn't just be gripped as is. I considered just putting a length
of heatshrink over the threads but getting it wrong and damaging the
threads would be costly in time and money.

Any advice appreciated.

Graham

p.s. Does anyone have any leads on short (<10") ballscrews with 1mm
pitch at low prices? Also cheap lead screw support bearings.