If they are anything like the old light up ones I remember from my youth, and therefore light as a feather, surely adding too much in the way of a circuit is going to mess with the balance making them hard to throw? They might make a better one these days, or you might be able to mount an equal weight of componants on each side mind you.
Surely it would be easier to mount tiny neodynium magnets to the inside of the rim of a yoyo, then throw it at an amplified guitar pickup circuit. Then you would get something weird sounding as the magnets span past the pickup, although I am not sure how close you would have to get to the pickup itself. If you can get something more complex to balance right, maybe you could use a tiny wifi enabled microcontroller to transmit values based on your LDR output or some gyro sensors to a companion module that turns it into proper CV, thus eleminating the need for wires to come out of the yoyo itself. Or do both, having the yoyo’s spin produce a waveform via a magnetic pickup that is then shaped by the values transmitted wirelessly from the built in circuit? You might need a really big yoyo to fit all that in mind you.