This article is from the Model Rockets FAQ, by Wolfram von Kiparski with numerous contributions by others.
From Chris Jennison
To keep nose cones from wobbling and coming out asymmetrical when using
an electric hand drill as a lathe...
Use a blank (dowel, broom stick or balsa block) 1/8 inch larger
(diameter) than the nose cone that you need. Drill a 1/4 in. diameter hole
as close to dead center as you can and push in a 1/4 in dowel. Dowel
length should allow the nose cone end to seat against the face of the
drill chuck. Find dead center by running the drill clamped in a vise at
moderate speed & slowly move a soft pencil toward the end at what
appears to be the center of rotation. After a couple of tries you will
find the center because your misses will draw concentric circles like
a bullseye. Now remove the dowel from the drill, clamp the shoulder end
in the vise and rough shape the nose cone with a file or rasp using the
marked center as a guide. Final contouring and finishing is done in the
drill with progressively finer sand paper.