It's a simple matter to clean up the knob on the lathe.
After cleaning up the diameter of the knob, we turned it and drilled a 5/16" hole. Next we drilled and tapped a 1/4" x 20 thread for a set screw to hold the knob on the bandsaw.
There isn't enough stub length to hold the knob far enough from the lathe chuck jaws, so a 5/16" mandrel used so the knob can be knurled.