"Mousegun" and "snubby" ain't the same thing.
In the US, .36Cal has always been considered a general purpose self defense bore, and has at various times (present day included) seen military use.
An NAA minirevolver ain't a snubby. It's a mousegun. A J-frame .38 five-shooter is a snubby. Same in six-shot .32Mag barely qualifies as a snubby, because that round is hot enough despite it's under-bore size to be a decent combat load.
A few Colt .31Cals shipped with no rammer hardware and a 3" barrel, but I'd still class those as mice versus snubs.
The Mormons were the first ones to chop serious defense gun barrels down to the 3" range. Mostly .44s, but some .36s too.
The various British "Bulldogs" and similar were a later riff off the same theme - cartridge guns in very weak .36 and .44cal (often rimfires). The Brits were probably doing the first DA snubbies. But the Mormons were doing it with percussion stuff decades earlier.