Interesting. STL is a pretty standard format for this sort of thing I believe, but you should really be asking the place that will do the cutting. Well, it's usually easy enough to convert files between different formats.
Most makerspaces, particularly with expensive equipment like (some) 3d printers, CNC machines, laser cutters, etc have mandatory training and the like before you're even allowed to sign up and use it.
There are lots of programs available that create file types that laser cutters will run, your makerspace might have a particular file type that they want to use, usually that will be dependent on the program types available on the computer that the laser cutter is hooked up to.
I would check on those things first, since any advice you get here may not be applicable at all to your unique situation.