We’ve had a chance to review this and cork is now provisionally approved for testing.
Please do some test cuts / etches. Check inside and have someone help outside to check how bad the smell is. Please report back here on Talk with what type of cork you try, how well it cuts and what sort of smoke / smell is produced.
As far as we can tell, there is nothing in the MSDS that is concerning, though that is for products with 100% cork. It is unclear if/what sort of binders or glue may be used in a cork product, and admittedly it is probably very difficult to find an MSDS for such an item. Cork is also listed and available for purchase from a few laser cutter companies (Epilog like you listed, as well as a few others).