There are two kind of people in the world: Those who have a lathe and those who don't. Unfortunatly I belong to the latter one.
Actually it isn't very comfortable to build the cone of a nozzle without a lathe. So I constructed a little tool like a pencil sharpener.
The two black parts are cylindrical milling cutters. They do not rotate.
All I have to do now is to put a M6 screw into the chuck of my drill press and to turn the lever. I guess even with a lathe it would be more work.