I can tell you from experience that my ugly lathe drill contraption is just that :text-lol:
It turns so slowly - I'll tell you, my wife's electric egg beater will work better !!! :banana-dance:
I use my wood turning lathe for making cribbage pegs using 3/16" dowell stock. Instead of the usual headstock with a pointed end, I mount a drill chuck in the headstock and use a collet that I improvised from a piece of copper tube with ~3/16" I.D. It works extremely well. The collet will work just as well in a drill chuck for your purposes. See attached photos.