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I agree that a Stanley knife will cut thin ply, but I've sliced my fingers too many times with them. I suspect I get impatient and try to cut too much at once. Lots of low pressure cuts is safer than fewer high pressure ones.

I usually use an electric scroll saw - the problem is you are limted by the size of the ply panel (whether it will fit into the depth of the saw body.)

For panels that are too big I've used a hand held jig saw and cut close to the line I want, but not right up to it. Then I take the excess out with a flap wheel - it eats away at the ply like a hot knife through butter and leaves a perfect finish.

If you decide to bond the polystyrene to the walls - make sure its a solvent free adhesive - the poly will disolve otherwise