Not sure why you want a square trackball hole but if you have a router it's the best for working with acrylic/plexi.
I would make a template with a hole sized the way you want it in a scrap piece of MDF. Then clamp your plexi over the template, with the hole in the required location. Then just plunge through the plexi using a router with a straight plunge bit, run it around the perimeter of the hole and you're done.