Small Bluetooth or WiFi-enabled remote button pusher?

This computer has to be rebooted once a week due to crappy configurations. I created a task already to boot it once a night but sometimes it needs to be turned off completely during the day. The computer is hard to reach and not in a place where all can reach.

The remote switches on Amazon seem to be a bit too large to fit back behind the TV where the computer resides.

Does someone have a commercial solution or even something that can be built with a small Arduino like the Nano? It doesn't even have to be WiFi or Bluetooth but anything that can be remotely controlled

Even some type of mechanical switch would make sense.