I haven't done it, but my hunch is if you shim the presser foot so it doesn't clamp down super hard right before cutting, that you could cut these on the paper cutter.
I would say the the PET paper is stable enough, and would cut well. I would just suggest leaving more space than typical if cutting apart with hydraulic cutter.
My idea though is to find a place that can perforate the paper, so that it can just be torn apart. Have a standard size for interior branding, and hats, and then those could just be torn apart, because cutting by hand is a bear and labor intensive!