Overwolf has been chosen by TeamSpeak to be their official overlay solution.
If no cursor is available, like in FPS games (CS:GO, CoD, Overwatch etc) hit Ctrl+Tab to switch between the game and control of the apps.
Press Shift+F2 to show/hide all Overwolf app windows. Pressing Ctrl+Tab will show/hide the Overwolf dock.
You can configure your own personal hotkeys in the settings window (right click the Overwolf tray icon and go to settings).
Good thing you asked!