How much trim space are you working with? None?
I'm sure you can find something thinner than the exterior insulation foam a lot of people use from Lowe's/HD (Tyvek?).
I think they also sell white styrofoam that is closer to 1/2" thick. I also think you might be able to find 1/4" somewhere, but I can't really say.
If you want to try to hide the foam, you should be aware that regular spray paint will melt normal styrofoam unless you do very thin layers spraying from pretty far away (so the paint does not get the foam really wet). I'm not sure what is responsible for the reaction, but I know from experience that it will melt it. I don't know if latex spray paint would be any better/worse or not.