I have done maybe 20-25 mouse hacks, and I always just get the ground from the buttons. It's never caused a problem, although I won't claim that it works on absolutely every mouse out there. Look for the common trace that runs to each of the mouse buttons. That'll be a little more tricky on your mouse because the buttons were on a separate little pcb, so you'll have to find the ground there, follow it to the connector, across the wiring, and to the pin on the main pcb. The good news is, you can just plug the connector in, and clip off all the un-used wires and leave the one that goes to ground, so no soldering for that one.
And don't sweat the Logitech thing too much- the reports of Logitech mice not working related to a different 4-pin opto that Logitech used to use. Newer Logitech mice use a standard 3-pin opto, just like yours. I haven't personally done one of those, but I believe it should work fine.