Does Nucleus work while using the BigPicture Mode? Maybe you can use they SteamVirtual Keyboard.
I haven't been able to get it to work, but in theory you can set your controller to open the Steam Keyboard.
For example the default config should be that if you hold the XBOX/Home button and the press R2, it should take a screenshot.
And with that it is theoretically possible to show/hide the virtual keyboard.
I should clarify: The "Show keyboard" option is not set by default like the "Take Screenshot" option is. But it can be added easily.