HI John,
I am guessing you intend to cut the shim rings from a sheet metal. I would assume the diameters don't have to be accurate. There are many ways to do this, and I think you should go with the one you can handle best using your tooling and equipment.
The way you're suggesting is very good if you can adjust the fly cutter for the required diameters. On a CNC mill it would be much easier - just using an end mill to orbit the circles.
If you don't have a CNC mill, I'd prefer making it on a manual lathe. The way I did it was to attach the material to the lathe face plate using double sided type and cut the circles using specially ground tool, but with 0.2mm I think you can use almost any sharp tipped tool. You could mount a piece of sacrificial plate on the face plate, even MDF would be good for this. Worked well for me in cutting 150mm diameter circle from 10mm thick stock.
Hope it helps.
Daniel