On the back of my PRS-600 there is a 5mm wide slightly shiny metal strip running from top to bottom at the hinge, or spine, side. The rest of the back is covered by a rubbery anti-slip coating.
The screws in question are indeed on the back of the reader. They're both on the shiny part - not the rubbery part, and are about 11mm down/up from the top/bottom of the reader.
I don't know how much of the reader your skin covers, but the entire rubbery part is what slides away from the shiny part. I suspect your skin covers the entire back, thus bridging the dull (rubbery) part and the shiny part. Otherwise, you'd be able to see the screws. You may be able to peel back just the area that covers the shiny part to get at the screws.
Good luck with your project. And if you find a replacement battery, please post the information here. I'm sure there are going to be other owners needing batteries as the devices age.
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