I used one of those cutters to make 'styrofoam' wings for model airplanes back in the early sixties - running off 240v mains with some filament bulbs to control the current. Boy, was I green about risks of electric shock in those days! The plans came from an "Aeromodeller" mag, I think.
The wire was from an electric fire element, and followed 2 plywood airfoil-sections at each end of the foam blank to form the wing halves.
It wasn't a success for me and I went back to the conventional balsa ribs, stringers and doped tissue.
All this was before analog or digital proportional radio control became available of course. You could run single-channel radio with a clockwork escapement giving a sequence of left-middle-right-middle-left etc....if you had enough dosh. I used compression-ignition engines [ with lethal ether and castor oil fuel - a laxative and an anaesthetic all in one can! ] or rubber power and free flight. I had pretty good legs then to run after 'planes as they vanished over the horizon if the fusee failed to tip the tailplane and stall the model after 3 minutes!
Happy days!
Alan