Is there a way to make projectors refuse focus?

[Dakas]

Reason for this question is to showcase an application in fullscreen mode with some inserts (like a camera showing the commentor's face) overlayed. If I don't want to waste another screen for the application in addition to the projector (which I record via HDMI), the application needs to run underneath the projector window and needs to react to events (mouse clicks, key entry). It will not do this if the projector takes key focus: the demo will work fine until you actually try doing anything. For most streaming setups, grabbing the application window rather than a whole screen is not much of an alternative since then all auxiliary windows (like file selectors) will not appear in the grab. I am currently making do by running a Xephyr virtual screen in a window on the same desktop as OBS Studio and grabbing that window, but it's a pain switching between the Xephyr window and OBS all the time when I need a change of scene. Having the projector window be impervious to events in its area would be the simplest expedient for a setup where I can interact with the projection as if it were the real thing. More complex would be a possibility to tell a projection where to deliver any incoming events (which would allows running the application on an entirely different screen from the projection and still interact with the projection).