I have not heard of any operational use of shotguns by the army in the Second World War or Korea. However I recall reading in the memoirs of RS Malone that when he was serving in army headquarters in the early months of the war the subject came up. He sent for the 'shotgun' file from the central registry. Eventually a dusty file appeared. The last entry was from the First World War. I will see if I can locate the reference, but I think the idea to use shotguns in the trenches again was overtaken by events.
As a point of interest (or not, depending on your point of view) U.S. Army infantry companies each had two M-1200 Remington 12 gauge shotguns on strength as company weapons. I can’t speak for current TOE but this was common from WWI up to the late seventies. Primarily used for guard duty around installations where a high velocity weapon would be inappropriate, ammo dumps etc. They were also carried in Vietnam by some troops who found them useful for clearing bunkers etc. I however always found this to be something of an affectation; a grenade was a better tool for the type’s fortifications we encountered and an M-16 a much more useful weapon.
I have done a fair bit of research into Small Arms at the Library & Archives. I thnk that I came across this same WWI file on shotguns. It contained a couple of pages, dealing mostly with the proposed acquisition of some shotguns from a leading sporting supplier in London. The idea was shot down (pun intended) when the possibility was raised that the shot may contravene the Geneva Convention. Canada did not use shotguns during WWII or Korea beyond deflection shooting training for aircrews.