Newpipe is my Android based YouTube player.
I don't have a Shield, but there are ways to run Android without a Google account. With a phone it's honestly not worth it because you're constantly messing around with side loading and stuff, but it may be doable with a TV box.
That said, I have an ancient NUC and run Fedora. It was a bit of a pain, but it's been years and years and it's still doing the job, and I'm told that it's gotten easier with the later releases.