To me the best plan would be having to bring only one chromecast with you from room to room, but I don't know how long or difficult it is to start up when you come into a new room. That may be easier than switching connections on the chromebook with a different chromecast in every room.
The problem is in occasionally forgetting, whether it is forgetting to remove the device or forgetting to switch connections to a different chromecast on moving to a new exam room.
