I have seen, what I consider, hacky techniques on my travels through audio forums. Mostly relating to digital streams, but the principle should still apply.
Instead of switching the inputs per-sae, enabled/disable/mute inputs and wire them all together. So when you want to switch from one source to another, it just mutes one and unmutes another. Mutes or Enables. If you have 2 I2S devices, it will pull the enable pin high on one source and pull it low on the next. The sources carry on playing, it's just their outputs are disabled and only one at a time makes it to the next stage.
In analogue audio terms a buffer opamp with gain of 0 or 1 for each input.
For video, that might also work, depending on the video stream and the opamps.