/cgl/ - Cosplay & EGL

I'm looking at making an arm sash similar to pic related for a con in may, but I'm an absolute newbie to sewing outside of some textiles sewing I did in school.

For the sash itself, I was looking at a plain purple sash like pic related that loosely covers the arm, with a white circle on the front side with a letter in the middle of the circle-

I have no sewing machine, so I was wondering what supplies would be recommended? I already have some fabric shears, but I'm worried about how I could create a perfect circle in white fabric without some sort of knife, but I'm not sure what kind I should be looking at. Additionally, is there any way to make the sash "hold down" the circle and the letter? I understand I can sew them with thread, but I'm slightly worried about them flapping slightly on the edges- while at the same time minimising the amount of stitches.

Any advice would be greatly appreciated, cheers