Well I can tell you, that if you can get your hands on some thin plexi-glass or acrylic, it would be MUCH better than a CD case jewel.
My suggestion is take the ring from the UMD door and put it on the plastic you intend to cut, then use it as a template and cut the rough circle out with a dremmel, trim it till it's a circle shape, and use a sanding bit to finish it off.
I've made blank jewels like this and my one piece of advice is to not rush it.