You would need to sideload it on to your shield tv using an app like ES File Explorer. If you Google "sideloading apps on shield tv" you'll find a ton of guides on exactly how to do it. Better than I can quote from memory at least.
As an FYI, I did something very similar (but with a VPN app called AnonymousVPN). My issue was that the vpn seemed to slow down my connection so much that I would constantly get buffering during videos. It was bad enough that I went back to PLEX as my main media hub.
For privacy-related matters, this is a pretty good resource:
>Went from no VPN to AnonymousVPN, and then later to iVPN.
I don't particularly like VPN apps. They're handy is you want to, say, circumvent a geo-block, but really don't do much for your security or privacy (I mean, you're entrusting your data to a third-party which may or may not be any more trustworthy than your ISP). I much prefer home-brewed solutions.
Recent Submission history for AnonymousVPN: