I’ve always used a mac mini connected to my tv. The imac will happily support a second display, is it far from the tv?
There are wireless devices that will beam an hdmi or dvi signal from one room to the next, but it needs to be hdmi2.0 for that to do 4k, and I’ve had mixed results with different devices recognizing the connection at both ends.
Another option would be an Airplay device like an appletv to cast your screen from the imac, and optionally your phone too, though that’ll cost a bit more than a good cable.
The chromecast ultra will do 4k and is a bit cheaper. I’ve only ever used the 1080 version of that, but I don’t see why that would work for streaming a 4k video.
obviously if you’re willing to compromise down to a 1080p connection it’s easier, a chromecast or the older appletv devices will do that handily.