Not quite what you asked, but I turned on the web cam, clicked the three horizontal lines next to the title to bring up the menu, undocked that panel, the closed the separate window. The webcam is still working, but its no longer visible (no dots, no face, nothing - but webcam is still controlling puppet. I then brought it back using the Window menu (selecting "camera & microphone") to bring it back. (Then had to drag title bar to dock the panel again.)
I don't know of a way to show only the dots without the face while streaming. I have not heard of anyone managing to do that.