iPad screen mirroring

I’m a teacher in a building where every teacher has an AppleTV’s for displaying their devices. I would love a shortcut, script, or anything that would make screen mirroring quicker. Currently I touch the icon in control center, wait for it load the 50 or so AppleTV’s in the building, scroll down to mine, and then select and wait for the negotiations. A Shortcut would be amazing.

if Apple or anyone solves this problem you will be this teachers hero!!