It looks like there’s a Lineage OS build for the shield, so if you want to eradicate google, there’s an option. It loses a fair bit of what makes the shield great though, since some of the audio and video playback stuff on the shield is proprietary to Nvidia.
I’m not sure about using it without a Google account, but you can definitely minimize their involvement. I installed flauncher, then disabled the default “leanback” launcher. Plex is installed from the play store but I side loaded an ad-blocking YouTube app. On a normal day I don’t see anything from or about google on my screen. I’m not sophisticated or, to be honest, concerned enough to know if there’s tracking or other telemetry going on. I mostly just want to avoid ads and moronic suggestions from them.
I use flauncher. It’s ugly and doesn’t have a lot of features but I don’t care. I only have two apps installed, so I’m rarely looking at or using the launcher anyway.
I’ve been using a Tex yoda ii for years and I love it. If you want to avoid leaving “home row” nothing beats a 60% keyboard with a trackpoint! I just bought a Tex Shura but haven’t tried it out yet.