Very thin sheet of plywood hardwood (Highbury Barn N5)

I have a lovely old chest of drawers but the thin layer of wood at the back is falling apart and has completely dried out. I would like to replace the back and have 2 sheets of very thin plywood hardwood (as in the pic), but need one more sheet or even half the width would do the job. A full sheet is around 1m 10/ 43 ins by 40cms/ 16 ins in width. Thanks so much if you can help.