Yes, Arduino Uno would be perfect. I just didn't want to assume you were an Arduino fan as there are many alternatives available and some people have strong views
I think this would be a fun Arduino project of reasonable scope. You'd only need something to convert the Uno's TTL serial to RS232 serial (either the 555-based circuit in the application note I linked before, or just a single MAX232), plus possibly something to convert the mouse's quadrature voltages into 0-5v (depends, the mouse may well already work at the right levels), and the rest is software. The logic would be very similar to the PDF I linked, you'd just have to figure out how to express it all in Arduino-style c++-with-Arduino-functions language. That said, you might need to avoid Arduino's digitalRead and digitalWrite functions as they are rather slow.