I use the TV remote control for the basic stuff. If I need to type something longer or more options, than I switch to Kore (official Kodi remote by the same developers). You just need the phone to be in the same network.
I’m not experienced with nvidia shield, but in my raspberry pi I use Kodi with the Daddy Live addon.
I believe you can install Kodi in the shield, so maybe that’s an option.
I use the TV remote control for the basic stuff. If I need to type something longer or more options, than I switch to Kore (official Kodi remote by the same developers). You just need the phone to be in the same network.
Never felt the need to connect keyboard+mouse.