Speaking as an old Navy Fire Control Technician who has shot a lot of 5”38 rounds, I doubt that a shotgun would reach a drone. I must say that I do not know the altitude that an operational drone flies at. One also needs to figure out how much to lead it.
A Predator MQ-1 has a service ceiling of 25,000 feet, a range of 675 nautical miles.
You’d need one hell of a shotgun to take that out. The AGM-114 Hellfire has a range of about 5 miles, and travels at Mach 1.3. 20 pound high-explosive warhead.
You’re gonna need a bigger shotgun.
When I was in the first or maybe second grade at Springfield Elementary in Panama City, our entire class got to visit a ship at the Navy base.
I am not sure if it was a Coast Guard cutter or maybe a Navy ship but I got to sit at the controls of a double barreled cannon. A sailor showed us the 3 round clips of shells they would dump in a hopper.
To me these were huge cannons tho I realize now they were pretty small. I do remember that even a six year old could spin the guns around with no trouble. Almost no effort required to move them.
I later worked with a couple of old Federal agents who were in the Navy in WWII. They told me they were Bofors guns and obviously anti-aircraft.
I wonder if kids of today get to have such fun at school. This would have been around 1953.