You could also always use a 1.25” hole saw and get some birch bark. The bark should be about 1/8” thick. You can either source your own or buy sheets of bark from Mudhole (other places may also carry it). Get a long bolt (12” or so) and some wide washers w/ wing nuts to make a handle clamp. Glue it up, clamp it tight, let it dry then chuck the bolt into a cordless drill and sand-lathe the bark to the final shape. Coat the handle with wax, epoxy, or varnish and you’re done. Mount the handle and go fishing.
I know you asked about cork specifically but birch handles are rare, unique, and beautiful.