Use a chamber guage to check the shell length. 2 3/4 shells easily fit in a 2 1/2 chamber and sizes weren't standardized until around 1930.
Stevens is tough to research due to lack of serialization and records and because Stevens shotguns weren't snobbish enough to interest fanatic collectors despite . I'd guess 1262 isn't a serial number but a manufacturing number to keep parts matched. Fluid steel indicates smokeless but keep the pressures low, please.