Along with the difficulty of making a clean switching transition,
your idea has a few other problems.
Whether or not they can be solved depends on your ingenuity
and the availability of hands-on help, which you definitely should get.
It would be better to use a manufactured video switcher that you can modify
to have the control circuit switch it from one input to another.
When you want a blank screen, the switcher should select the output
of a raster generator (a DVD player in stop mode may be sufficient for this).
When you want an active video signal, have the switcher select that source.
Also, never cut into video (or audio) cables.
Instead, use a project box with suitable jacks mounted in it
so that all cabling can be easily disconnected from it.