One option I didn't see above: sometime around the late 1940's, Savage/Stevens made their single barrel shotgun in some models with a hollow mottled brown plastic stock. I think the plastic was called Tenite. The first real gun I ever fired was one of these in .410. Got a lot of squirrels with it later on, too!
I've seen some in 12 ga, & bet they made some in 20 ga too. If you could find one in 20 or 16 ga it would be ideal for your purposes. But a new Rossi or other inexpensive single barrel will be a lot easier to find!