Hi Mike,
I have just opened my Sony FM/AM Radio ICF-P26. First remove the two screws were the batteries go.
Then as gently as you can using a very small flat screw driver beginning from the bottom left side were the Fm/AM/OFF switch is, try gently forcing your way up, there are a few hinges that will pop open. Once you get to the top, just above the tuning dial, repeat on the opposite side, where volume and earphone go.
Good luck! Even though I was doing it as gently as possible, I left some small marks on it, I guess it will be hard not to...