If it is just a switch, may as well give you more than 1 hdmi in and allow the dedicated card to run into the switch(allow a jumper or similar to swap from onboard to this extra hdmi in.).
This would allow the dedicated card to do what it does, while still letting the system use the feature when off.
So you screen would ALWAYS be plugged into the board, but the dedicated would also be plugged into the board to allow its signal to pass to the screen when needed as well.
Low power and still gets the job done