maintain a switch position when arduin is off/sleep mode

I have not tested over a long time (trying now, and you seem to be right), but refreshing it every minute or so if fine, the arduino will need to wake up to make a measurement anyway.

4.5V is plenty too, it only needs ~4V to go fully dark.

But if I put a diode in series, how will I blank the screen?

Ive considered a relay too, but doesnt a relay need to be powered to maintain its on position?