Last remarks before I stay silent (not having actual experience with photo mats): Perhaps a drag knife is a good approach? Needs a bit of tinkering: Snapmaker Vinyl Cutter Attachment
As for blackening: That is certainly happening, have done my bit of cardboard laser cutting. However, with a cloth or even your bare fingers you can remove most of the soot and get it “safe” - however, perhaps try it first on something not too important/expensive…