Two ideas ...
1. create a serial mouse. Most micro-controllers can be made to use RS232. If Windows will accept a serial mouse connected to a USB/serial adapter, then an Arduino should also work.
2. Use the same Atmel processor as the Leonardo and Beetle. ATMega 32u4 interfaces directly to USB. You will need to replace the boot loader or at least modify the boot loader to have a PID/VID that matches a generic USB mouse. Obviously, you will also need to write code to mimic the USB interrupt transfers. It's a mouse so you don't need Bulk or Isochronous USB I/O.
Microsoft's WDM driver DDK may have sample USB mouse drivers that you can examine to get an understanding of the Interrupt transfer packets. Also, there are tools to inspect USB traffic - allowing you to see the messages from a generic USB mouse.