Send Keystroke to both Server and Client Machine

[Cid]

Looking to see if it's possible to have either a keystroke (or side mouse button) be broadcast to both server and client, regardless of which machine is currently active.  Setup is this: server PC has a game fullscreen.  Client PC has Teamspeak and other support applications running.  Want to be able to press a Push to Talk key and have it be sent to the client machine even if the server is currently active (or both machines, as the PTT key is mapped to nothing in the game).  Any help would be much appreciated!