If Teamspeak 3 allows you to set custom keyboard shortcuts and you assign very unique shortcuts (e.g. Ctrl + Alt + Shift + P) then it will be unlikely that any other program uses that shortcut. Yes, if you're typing at exactly the same time as the keyboard shortcut is sent then you will interfere with the shortcut and vice versa but the Arduino can send the shortcut very quickly and if you're the one pressing the button then likely you would not be typing at the same time anyway. So I really don't see why this is such a concern.