If I were looking for a lightweight tag along, that's accurate enough for small game hunting, I'd look to a S&W Kit Gun. My 39 year old S&W Model 43 Airweight Kit Gun (15 ounces) will give a pretty good account of itself.
Beautiful 43. I have a few Kit guns but no lightweights, and certainly nothing so nice looking. But they are my favorite pack-alongs.
I just found a 63 to add to the mix.