it is still a bit of a puzzle but I get the impression you are wanting to perform an interactive presentation where the person's hands can be used to manipulate the image.
I can reasonably assure you that you are approaching this in the wrong manner. Your idea appears to be to shut off the video signal for a very brief interval so that you can capture an image of the hands in uniform light with the camera during that brief interval.
There are many reasons why this is impractical. In particular, the projector cannot be blanked in that manner as it uses a "frame buffer" which holds the image while it is being drawn, so any interruption to the "drawing" process will not suppress the image. This was somewhat more practical when CRT displays were used because the image was not retained to such a great extent as the raster scanned across the screen. In fact, they could even be used as a "flying spot scanner" to actually take a picture where the reflection from the target was detected as the spot scanned across it.
Secondly, a common video camera does not necessarily implement a shutter, though digital ones may, so you would need to control the camera precisely in order to capture the image at the moment of your blanking of the projector. This is vastly more involved than just using a CMOS switch to interrupt a video stream.
Finally, the flicker in such a process as you have imagined would always be apparent. In particular, in order to take a picture, you would have to not merely blank the projector video, but flash it full white. That would always be apparent and even if happening repetitively and regularly, say at 100 Hz, it would have the effect of "washing out" and reducing the contrast of the remainder of the video.
I think you will find that the commercial systems for doing what you propose, do so either by matching the camera's image against the actual dynamic projected image and detecting differences, or else use an alternative means of locating hands and other objects near the table, such as infra-red.