The problem is not with your equipment, the issue is with the CW app, it is not designed to airplay to apple tv, which, I think, is on purpose. If they would have given us an apple tv channel 3 years ago when it was rumored, then it would work, but, they are not on board with us at all. At some point after CW was supposedly in talks w/apple for an ATV channel, they also dropped their channels from some of the cable/sat companies...they just don't want people to watch CWHello from January 2016! No CW app available on the Apple TV 4.
I've tried streaming from the CW App on my iPad Air and using AirPlay to the Apple TV, but that is hit or miss. I don't know if my AirPort just can't handle the dual jobs, but the video on the Apple TV drops out (leaving the audio) or goes to the Apple TV home screen. I can start it up again, but after a while I get aggravated and just watch on the iPad.