I agree with the statement above: Use your router for this. Cutting small circles isn't the easiest task, but you can make yourself a helping construction:
1. use a sheet of thin plywood (5mm or so) maybe 20 x 20cm. Drill a hole in the center of it (almost, no need to be accurate here), where your router bit (use a rectangular shaped one with a diamater of about 3 or 4mm) will fit through.
2. Screw the plywood under your router, preferably in a way that you can reach the screws from the upside. Don't allow any parts of the screws to outstand out of the plywood. Routers usually have some holes or whatever is needed to do this. Measure the needed radius from the farest outstanding corner of the bit to the opposite direction and mark the center of the circle.
3. Unscrew the plywood and hammer a short nail from the upside through the center-mark and in the center of your later trackball hole.
[edited: Oops. don't nail in Plexi. Drill a small hole.]
4. Mount the router, and cut the circle in at least five turns.
If you coudn't make a construction where you can reach the mounting screws from the upside: Mount the plywood with nail to the router and press it (hammering isn't so good for your router

) on to the center. Or drill a tiny hole in the center where the nail will fit in.
[edited: same here. don't hammer in plexi. drill a hole]
Before doing all this, check the manual of your router if there isn't already a solution for routing smaller circles. Mine has it.
As an alternative you can use a copy mask and cut the hole out of thick cardboard first. I have little experience with this and my results with copying have never satisfied me, but with a simple circle it should do well.
Try it on some waste material first.
(Hope my english isn't too bad)
RubbrDug