In the woods, you gotta use the rod that's in the gun.
At the range, I use a muzzle protector cone that fits in the crown of the muzzle. The rod is steel, polished. Hardly ever touches the sides of the bore.
You could make up a steel rod from thin-wall tube, so weight would not be such an issue. Braze solid plugs in the ends. One end could be 8-32 or whatever thread you like.
Example: from McMaster-Carr
9220K331
Smooth-Bore Seamless Steel Tubing, 3/8" OD, .305" ID, .035" Wall