I use a G25, so part of this may not apply. Just go into the Settings, Sound Input/Output Settings, set it as something like CTRL, go into the Logitech Profiler, click the button, make a command, and set it to work every time Race is running, then whenever Race is open it sets that key binding to work.
1/ Choose a button on your wheel that you'll use to activate the mike.
2/ Go to teamspeak and select "Settings", and then "Sound Input/Output settings".
3/ Choose "Push to talk option" and bind it a keyboard key that you do not use in the game. Let's say you select the " F " key.
4/ Go to jbdinx and bind the wheel button you want to the F key. Let the program run, don't close it, and then test the whole thing.