Do you have the version 4.6 drivers?
If so, open the Logitech Profiler. Then go to Options and Global Profiler Settings and check Apply Persistent Profile. Then come out of the Options to the main screen. Click on the button you want to assign and Select Command
, then New Command. Give it any name and click Record, press the keyboard button you want for TS (check what LFS has keys set to so there are no clashes - don't worry you don't need to press the keyboard once its working) and then click Stop. Click OK and the button should be set so that when you press it (I use O, you use X), the PC registers the keyboard button you recorded being pressed.
Then go into Teamspeak and set the Push to Talk button to the keyboard button you specified. Et voila...
An example...
I go into Teamspeak and set Push to Talk to 'R' on the keyboard.
I then go into the profiler, ensure Apply Persistent Profile is checked, and record a New Command to button X. The New Command is simply pressing 'R' on the keyboard. Now when I press X on the wheel, Teamspeak sees it as 'R' being pressed on the keyboard and I can talk.
Let me know if you have problems.
P.S. - I would guess the same thing works for F9 and F12