I will err on the side of a longer knife if I only get one.
This has never happened to me...in decades of camping, scouting as a Boy Scout, an Eagle Scout, and a decade plus as a leader on Scouting Trips.
The last 20 mile day I did, I did not take a large fixed blade because the area I was in, we were not allowed to cut any foliage. The camp area was well established. And Opinel and a more robust locking folder were taken.
(I was going I to a known area, where at the end of the hike the food and other supplies were waiting).
I can't think of another overnighter hike or canoe trip where I only had one knife...
Typically, where I will have a light saw, a fixed blade, and a few folders for details work.
Often it is a tomahawk, a smaller fixed blade and a folder...
or a Machete, a smaller fixed blade and a folder.
But your poll, your imaginary rules, I guess.
A larger fixed blade will cut notches in sticks just fine.....
Small game like Rabbit, and squirrels and fowl don't really need much knife work.
You had asked how someone would hunt squirrels with their big knife? How would you hunt them with your small fixed blade? It is a non question..... the answer is neither.
You use a throwing stick, or a Spear, or a Spear thrower (Atlatl), or a stick bow (if you are really out surviving I guess).
Even the lowly rock is preferable to "hunting" small game with a knife... were you planning on throwing your knife? Or running small game down and stabbing it??
I don't always bring bigger blades (because I will pack a fast cutting arborist saw), but it is normally an "and" situation.