Ok, I decided to just jump in and do it today, and it's not as bad as it seems. The power switch doesn't have a connection to the inner workings of the reader at all, so it's a pretty simple in and out swap. I've attached images for the screws that you need to remove. I used the silver shell for the images because the dark blue made it hard to see where the screws were placed.
I'd suggest doing it against something white or very light colored so you can find the screws easily. Magnetize your screw driver tip, it will make it easier. Pay attention to where the screws came from, they are different lengths, so sort them however you need so you know which length goes back where. Have some sort of small container to catch the screws in, they are impossible to find if you drop one or it rolls away.
Remove the side trim and the back of the unit as shown in the video Mark Nord posted above for battery replacement.
Then remove the top trim piece. There are 2 screws holding it place, one from the back of the unit and one from the top. Pry it off gently the same way you removed the side trim. See image Top trim.jpg.
Next remove the 8 screws along the side of the front shell. There's 2 along the top edge, 3 along the side, and 3 along the bottom. See image Side screws.jpg.
And finally remove the 5 screws holding the unit against the front shell. There's 3 along the top and 2 along the bottom. See images Front screws.jpg
and Front shell screw holes.jpg.
From this point, gently lift the free side of the reader up over the edge of the front shell and gently remove it out from along the solid edge. You might have to wiggle it gently to get it out of the U-shaped channel, but it should come out pretty easily.
Now just reverse it all and done. The hardest part will be replacing the screws in the holes that are nearest the magnets, at least that was the hardest for me. And I did manage to drop a screw, but I used a strong magnet moving it around likely spots and found it without too much trouble.
My blue reader with the horrid screen is now like new with a perfect screen. I put the bad screen in a slightly scratched silver shell on a used reader I got for $35.00 recently just for this purpose.
Edit: Just to keep all info in one spot, here's a link to the Service Manual for the PRS-350
that might help you also.