I was looking for a way to turn my android phone into a bluetooth keyboard and mouse, which was unsuccessful without root. However I found InputStick which looks like it would work well enough.
InputStick is a USB device that has bluetooth, which your phone connects to. The device InputStick is connected to thinks that a USB keyboard and mouse have been attached.
Has anyone used this with a Nvidia Shield TV?
If it just emulates a standard USB keyboard and mouse, like the website says, then there's no reason why it wouldn't work with the Shield.
But why not just use the official Android TV Remote app instead? The only thing you'll lose is the mouse emulation, which isn't useful unless you're sideloading apps.