Cutting wood certainly creates fumes. You are burning it. I have my laser in an enclosure with an extractor fan pipe outside my workshop. I wouldn’t consider cutting wood without active ventilation.
A cheap diode laser cutter is all you need for 4mm ply, provided it is laser cutting compatible. The glues in some ply can be problematic unless you have a powerful laser. I’m actually cutting 3mm ply at the moment for boxes to hold screws. I had a 3D printer so just added a diode laser to...
These had a lot of exposure five or six years ago. At the time there was a video from the manufacturer showing a lot of detail. I’ll see if I can turn it up.