I just happen to have a nice supply of different heat shrink films (I believe it’s polystyrene), including the Grafix Gold specified in one of the Featured Designers offerings (it’s this one). So I thought I’d give it a go in the Aura. Turns out it cuts like butter! Speed 60, power 2, one pass.
Black cuts great using the same settings. Opaque white and inkjet printable white barely tickled the surface. I could get partway in by cranking the power to 10 but the result was not pretty and not usable in my opinion. The clear and the sanded clear were not touched at all. So I would conclude that your film might be cuttable if there is substantial coloring embedded in it, but not otherwise.
I would say even if you could, that would not be an efficient tool for the job. The best results for heat shrinking come from even application of heat and I don’t see how you could do that with the tiny dot of a laser.