One of the things I've done when I didn't have any mylar is to make a thick template using freezer paper. I iron 3 or 4 layers together and then cut my shape. You can do the running thread thing, spray starch and then remove the template.
I like the method where you sew backing fabric around the circle, then cut a slit in the backing fabric and turn it inside out. There are lots of ways to make applique circles that don't cost much of anything.