Cast to chromecast from phone without wifi

So, I'm a Senior in high school, and we have a senior privilege lounge, there's couches, but most importantly, a TV. It has one unused HDMI port. I want to install a Chromecast so I can wirelessly play video. The school's WiFi blocks basically everything, so that isn't really an option. Is there a way I can cast the screen of my phone or cast local content directly from my phone to the Chromecast? Or does there have to be WiFi? I could bring in one of my old routers if you think that would work, I just want to keep it as simple as possible. I'm looking for the easiest solution once it is in place, I don't mind some complex setup stuff at home.

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