I think this is a really great idea but i would save anyone the labor of shrinking the heatshrink and then trying to thread it off and cut it and put it back on.

rather i would put between the felt cord and the heatshrink.. whatever it is that you intend to use to mechanically fasten it to the ballscrew nut. i would not worry to much about the cord unwinding, though you could sew it to itself at the end of the coil. far as i know the adhesive on headshrink is the same stuff used in hot glue sticks so you can always add more.

a small amount of superglue could hold the felt together while wrapped around the screw, before you shrink the heatshrink.