Johnson Plastics sells a faux leather intended for laser cutting and engraving. It comes in four colors. It’s extra floppy and a bit stretchy, but it works very well and is pretty cheap. What is not cheap are their shipping rates so if you live by one of their outlets picking it up would save some cash.
Their website is not user friendly, but going to their website and searching saddle collection will work for you. There are also examples and discussions of saddle collection faux leather on this forum. @roxygirl7711 this thread contains settings Janerlea used for the Johnson Plastics material. I would not be surprised if the materials are very similar (or identical.)