I was referring to the riot gun shown in the photo, not a skeet gun. Clay pigeons are a challenge with a handgun, and shooting rounds into the air is dangerous.
On the other hand, my best one-shot with a pistol -- squirrel at 85 feet with an 1860 Colt Army cap and ball revolver (excellent sauteed in butter and bourbon over an open fire), shot made from the sitting position; second best one-shot with pistol -- head shot (popper, not human) at 85 yards in broken terrain with 3 inch S&W610 using .40 S&W 185 grain jacketed round, tactical scenario, kneeling; best one-shot with carbine -- dead center at 600 yards with Colt AR15 carbine, M4 16 inch barrel, open military peep sights, and 69gr boat tail hollow point match ammo, NRA High Power Match, prone; second best carbine shot -- center mass at 425 yards, uphill, in a tactical drill with the same AR15, kneeling; fastest Dozier drill (5 shots on 5 targets at 35 to 45 feet, from the holster), standing -- 5.4 seconds; highest score in drills -- 48 out of 50 with the same 3 inch S&W610. So, perhaps a clay pigeon is still possible. God smiles on the Irish.