Always wear safety glasses when cutting, drilling or punching.
The bobby pin is a little heavier gauge than recommended for the punch, so use a drill if you have one, or punch very carefully (and be sure you know where you stored your replacement pin).
Lay the sprocket and 25mm round blank on top of each other; use center punch to mark exact center of the blank. Punch or drill the blank.
Lay components together, and rivet. The 1.8mm punch makes a hole a bit bigger than you really want, so this rivet is a bit tricky to start (if using plain wire). Do just a few taps on one end of the rivet, then flip to the other side and repeat frequently to make sure you keep everything centered.
There isn't much room on the backside of this bobby pin, for your hammer. Even if you normally prefer to rivet with a ballpeen hammer, you will need the thin end of a Swiss-style hammer for the rivet on the back of this bobby pin.
When the rivet is finished, use a flat needle file to texture the surface of the sprocket. Not only does this give a nice slightly sparkly texture, it also hides slight imperfections from the hammer hitting the font of the sprocket (whoops). With a flat or triangle file, you don't have to worry about accidentally marring the nice brown surface on the Vintaj layer below, like you would if you used sandpaper or steel wool. And you can still get up nice and close to the rivet. When you reach the desired texture, seal with Renaissance was, and buff with a soft cotton cloth.
1 half-gross (use 1 piece) #30-822-7 Antiqued Copper Plated Bobby Pin, 10mm Round Pad