Bamawife, for example, cannot manage a shotgun, she's quite petite.
I've found that size doesn't matter as much as attitude. Particularly determination. However there are physical limitations no amount of will power can get past.
I'd be willing to bet Bamawife could manage a shotgun, though probably not in the "approved" manner.
I base this on personal experience, with my mother. She was 4'10" (and a half! dammit!!)
Wore a size 3.5 ring, and only broke 100lbs during her pregnancies, barely...
She couldn't rack the slide on the Ortgies .25acp Dad got for her, she lacked the grip strength, combined with the small area to be gripped. She could rack the slide on a 1911A1, if she cocked the hammer, first. She could shoot Dad's S&W Highway Patrolman .357, but holding it up at arm's length was a struggle.
She was a crack shot with her .22 rifle and Ruger super Bearcat, neighbors nicknamed her "Annie Oakley".
She could manage her father's Ithaca 12ga SxS, too. But not in the usual way. She didn't shoulder the gun, she shot from the hip, and rather well. She joked that Victoria Barkley taught her (The Big Valley). She would explain, her technique was simple, just grip the gun firmly and let it "swing" her arms back during recoil. She couldn't wing shoot that way, and didn't bother, but any ground target within about 40yds was dead meat, including small fast moving ones (running fox).
It can be done. OF course its easier for some than for others. As an 8yr old, I watched her face down, corner and hold a rather pissed 600lb Angus bull with only a pitchfork, for a half hour or so, until Dad got home and both of them could get him back in the pasture.
If you can't physically do something the regular way, AND you are determined enough, there's almost always a usable "work around".