Vinyl, which is a very common material for records, is toxic when laser cutting. Do not use it in your laser cutter! A better alternative is to use thin, black acrylic. Another option is to use thin mdf and paint it black. Either way you can "engrave" the lines with a low power vector cut and add a label to create a nice record effect. Much safer and no records are injured in the process.
A user, Amanda Grant, recently shared this video after cutting a couple of vinyl records. Within days, the machine went from like new condition to this.