True from a barrel length POV, but obviously...capacity is the other factor.
Unless the grouse where you're hunting are so dumb you could hit them with a rock...I think short-barreled shotguns are a pretty poor choice. I also think the pistol grip/raptor grip shotguns are a poor choice for anything at all, and shooting them has a fun factor of about 1/10 for me. lol (And I'm a big guy, not recoil shy) When I read questions like these, I wonder how much shotgunning experience is at play...because in my hunting experience, most birds are very skittish...wing shots are about all you get 80% of the time..and most of THOSE encounters are too far off anyway. (flushing 100+ yards out) Lugging around an un-choked, 12.5"-14" barreled shotgun where I hunt would likely only reward you with a nice walk through the woods, but no birds. Not that I score very often either.

The shortest-barrel/no-choke gun I've ever used with success (wing shots and sitting birds) was a 21" barreled 870 Wingmaster in 20ga.
There are small/light guns that excel in applications like this, even the lowly Cooey 84. lol (I have one in 20ga) These could not be more simple/reliable/easy to break down, etc. I get wanting a pump, so my suggestion would be something like a Mossberg 500 (lower weight than an 870) and if size/weight is still of concern, maybe opt for one of the models geared towards women, or younger shooters. It'll have a vent rib barrel, interchangeable chokes~real benefits when looking for birds. If the LOP is too short, the receivers are always shared with the full-sized guns...so you could carry a youth-sized gun, with an adult-sized butt stock to make it fit better. We have an 870 Youth (laminate stock) Express that I really like, has a 21"/VR barrel. I'm 6' 1", and this compact pump gun fits me just fine. In the event you're looking at a Remington...just keep in mind they have 3 sizes. The barrel and stock set sizes are different. The compact (18-1/2" barrel, but impossibly small butt stock) youth (21") and full-sized (26"/28") It's the "Youth" I'd suggest to keep the size usable, but still compact.