I understand the reasons your not wanting a screen on the device, but if your having holes for buttons - and in theory to let the sound out of the case for a speaker.  How about something like EInk - these screens are very power efficent as they only need power when the display changes.  And they are creepy solid, you can cut them and they still work.  I have an old ereader that has dents in the display and it still works no problem.

https://www.adafruit.com/product/1347

Thanks for reading.

kc1cxx