Conrad:
As one of the old-time engineers who still makes drawings 'on the board' rather than using CAD, I can appreciate your wanting to keep the Dietzgen compass as original as possible. Dietzgen was once a real "engineering supply" firm, offering anything from basic drafting supplies to surveying instruments. A lot of the drawing instruments used to be made under their label in Germany. That being said, I will offer my own 'two cents' as to how the thumb screw was likely made:
Dietzgen (or their subcontractor) used a 'poor man's press fit' which let them get by without holding the closer tolerances that an interference fit would require. Back in the day when the drafting instruments were made, things like "Loctite" were unknown. From the appearances in your photo, the stud was made separate from the head of the thumb screw, and there is a slight gap surrounding the stud where it enters the boss on the head of the thumbscrew.
I doubt that the stud was threaded into a tapping in the head of the thumbscrew, as it would then have been necessary to lock the threaded connection. Otherwise, use of the instruments might have unscrewed the head from the stud. Without Loctite in those days, the option would have been to "sweat' the threads together with solder to lock them permanently together.
Given the fact this was a small part and likely being produced in large numbers, I doubt that any soldering/sweating was done to secure the threaded stud into the head of the thumbscrew. Rather:
-the knurled head of the screw was machined as one part, with a hole drilled into the 'boss'. The diameter of this hole was 1,8 mm or thereabouts. The knurled head of the thumb screw was made in an automatic screw machine in one set of operations. After being parted off, it was held by the boss in a collet to allow the decorative facing of the head of the thumb screw to be done. This eliminated any burr or center tit from the parting-off operation.
-the threaded shank of the screw was machined as a separate part, call it a stud. The stud was machined from 1,8 mm diameter stock. One portion of the stud being 'fine diamond' knurled. The remaining portion of the stud got threaded. Easy enough to do in an automatic screw machine.
-the fine diamond knurled portion of the stud was then pressed into the 1,8 mm drilling in the boss on the head of the thumb screw.
This was a quick way of fastening or locking the threaded stud into the head of the thumbscrew. No close tolerance machining, no tapping of the head of the thumbscrew, no sweat/soldering.
Heating with the hot air gun is not going to break any fit between the thumbscrew head and stud. You will likely have to drill out the stud. A new stud can then be machined, and you have the luxury of setting it using something like Loctite 'cylindrical parts fixing' compound (603, I think, a 'green Loctite' which I use and find to be quite effective on little parts like this one). Getting centered to drill out the stud is a matter of what machine tools and tooling you have at hand. You can open the hole a bit more and ream it to any convenient size, then size the unthreaded end of your new stud to fit.