Here is a (almost) fully functional red dot sight. it's not like i'm trying to outdo everyone elses guns at the works Christmas party. It's designed on a Nerf stryfe but would probably fit other stuff too.
When i say almost, i haven't got the concave lens that eliminates the parallax and keeps the dot on target when you move your eye around. It just uses a flat piece of perspex which doesn't matter as the Nerf gun is anything but accurate. Plus i don't have a red LED so mine's white. Other than that it's flawless. If you can sort out a curved screen good on you.
I have scavenged everything needed out one of those POS solar garden lights from last year that no longer works (it's only the battery that's dead). if you get one with a sliding switch you'll be golden.
Shout out to Andy Williams on GrabCAD who provided the "Red/Green Dot Holographic Sight". it's an AC inventor model that i couldn't open but i was able to view the STL in Solidworks to get a few dimensions. nice one Andy.
Black plastic and a brim is probably a good idea.
if you rotate the "red dot top" 10° around the X axis, it'll sit flat.
(step 1) important
you will need to drill a hole for the light to shine through. if you drill from the inside out, there is sort of a pilot hole in the bottom of the big hole for the LED. start small and get bigger if required. i have drilled a 1.5mm hole.
(step 2) you need to remove the tabs circled in red on the base part, they're only for support as i use slicer.
(step 3) you may need to paint the inside and/or the outside black to hide the glow of the LED through the plastic.
(step 4) glue the sliding switch up font so that the handle bit protrudes through the hole. once dry, you can assemble the two halves of the dial so when you twist the dial it flips the switch. damn right it's working dial on top!
next, you may need to extend the wire from the switch to the LED if it's short. glue the battery terminals into the base and insert one AA and screw the two halves of the case together with some M3 screws.
(step 5) now the hard part, the screen.
you'll want some reasonably thick scratch free something. I've finally used some 1.5mm perspex but was thinking of possibly cutting up one of those clear plastic Christmas baubles with stuff in it for that magic concave shape.
anyway, trace around the inside of the frame and cut it out. then sand down to a perfect fit. you're going for a screen with a slight backwards tilt almost vertical. you'll know it's right when the reflection of the LED is in the middle. glue the screen in once done painting.