When I spent some time on a Ward 2a capstan lathe back in the 1950s, the cutters to reduce screw shanks to size were known as hollow mills,and mounted in one of the turret stations,ok for fully threaded screws but not brilliant at producing a good finish on a plain shank,despite stoning the cutting edges,threading was usually button dies for for smaller BA sizes and self opening die heads for 1 and0 BA . If you need to turn a long thin screw shank make the screw a bit longer and centre drill the end and support the screw shank with a small centre,then reduce the length to remove the centre or use a travelling steady,for small dias use a home made steady device to fit the tool post.If only a part of the shank is threaded,hold the material in a collet with just enough protruding for the thread,turn down the length to be threaded ,thread it then feed the rest of the screw shank forward and turn that down,