My first few hand drills were made with wood, but I recently made a new drill by simply wrapping paper around my drill bit until it was the desired thickness, then gluing it all together. I got better results with this method than with the drilling.
The following instructions should create a perfectly centered and perfectly strait hole in the center of a 1/4“ dowel. The drilled dowel becomes the handle for the nozzle drill.
Now you have perfect drill handle. Take out your smaller bit and glue it into the handle.