Hold the drill body in a four jaw chuck with copper blocks between the jaws and drill. Indicate at the large end of the taper, fo to small end indicate. Tap till straight. Repeat if required till running true. Dress up center if nicked up. Place live center in tailstock. Have at it. To cut the Taper set up the taper attachment if you've got one before you even start otherwise set compound at appropiate angle making sure the tool is on the center height.
Forty plus years and I still have ten toes, ten fingers and both eyes. I must be doing something right.