The hangers are the part that swivel that the button attaches to. I'll add a picture of a hanger. I've not made and spurs out of rasps. They're not really my style and I don't want to spend the time grinding down bands to a suitable thickness. What you say about the shanks makes perfect sense though. If I was going to do that, I'd anneal the pieces of rasp that are to be the shanks then rough them out with the harbor freight portable band saw. Then I'd tack the two pieces together and grind them very close to the final shape. Then I'd weld the edges with a wire feed if available. What ever method you choose for welding, I'd use plenty of anti-splatter spray. After the weld, anneal them again so the metal doesn't end up too hard to drill the hole for the rowel pin.
As I said, rasp spurs aren't really my style but I've seen a lot of them both good and bad and can offer a pointer from what I've noticed on the better ones. Pay attention to the direction of the teeth. Make sure the teeth go the same direction on each side. If the teeth on the outside of the bands cut towards the rowel, make sure the teeth on that side of the shank do the same. If you are using one piece for the band, the teeth on the inside of the band will cut towards the toe of your boot and that side of the shank should do the same. The best looking rasp spurs I've seen are made of two halve connected at the shank and all the teeth, inside and out, point in the same direction.
In my opinion, you want your band to end up around 3/16" thick but using a steel like a rasp might allow you to go a little thinner for a lighter spur and still have a springy band.
Ben
Outside of hanger on a purchased set of spurs
Inside of a hanger I built.