Bonanza:
The bigger the shotgun-action you can use, the better. Not because you need strength, but because you need weight! A .577 light nitro or BP double needs to be up around 10-pounds to be comfortable to shoot all day, and you can't get that in a 20-bore frame unless you keep lots of weight in the barrels themselves. Heavy barrels kill the handling completely, and the gun will not be 'lively' to shoot. A quick-handling double simply must have most of its weight between the hands, not out in front of the forward hand.

A heavy action and light muzzles is the secret!