You don’t need the screen to choose the OS, you can choose it with the keyboard too:
For switching the OS (if you’ve booted the last time into windows and you now want to go into android) you click left arrow on the keyboad and then enter.
For going to windows, if you’ve booted to android the last time, you click right and then enter.
For me this works with the keyboard dock, but I think it will work with an external USB keyboard too.
I hope, that I I’ve helped you, if you’ve got other questions, feel free to ask me.