I want to know how large to make a snare in relation to known skull sizes of various quarry, specifically grey squirrels. Common skull size of a grey squirrel male and female (no dimorphism) is zygomatic breadth (width) 34.5 mm; cranial height in vault of skull (height) 28.4 mm.

Some of the answer to that question is....how wary are grey squirrels ? They probably won't shy away from tight spaces but they might.
I think I would start with a loop of 2-2.5 inches. If you get refusals, open it up a bit more. Also consider how high the bottom of the loop should be. Is this on a run pole ?

Our squirrels in Alaska aren't metric, however, so your results may differ

Height of the snare is more important than the loop size. This goes for every animal. Gotta get the loop to hit its chest. Loop just needs to be no smaller than the skull plus ears.

Most trappers make their loop too big.
Go double snare diameter,or a touch more, to diameter of skull.
For example for fox the skull diameter is about 2 1/2 inches,snare 6 inch diameter is perfect.Some trappers like to go 7.Myself and others think 7 is too big a loop for fox.

5" inches or 10 will kill fox. Just as long as the bottom is at the right height

No,they will get a leg in or worse two.
I would much sooner have a snare or two knocked down and catch him in another nearby snare than have a bad catch and possible damaged fur.
Fox are very catlike,and lots of trappers set snares too high also.
Bottom of snare-6 inches for cats and fox at jackpot.
I have seen lynx go right thru an 8 inch loop without touching it,worse than fox for flank catch if loop too big.
Set too high at a jackpot you will miss them-they go right under.
Trail snare is different,need loop higher a couple inches for lynx but still small loop.
Fox a bit higher too for trail snare.

Leg through means your snare is too low. I would rather miss em going under than let them set low.

Letting cats go through is a plus here

Wrong-I set all snares low as taught and never get leg in.
Leg in is from too big loop.

I respectfully disagree with you Boco. A fast loaded snare that is high enough to hit them just under the chin is gonna close fast enough to get them right around the neck.

To the OP's question I don't know anything about snaring squirrels since due to our regulations I've never had opportunity to try.

Big loop,low-lots of Ghosts.
Big loop high-lots of misses-knocked down snares
Small loop too high they go under
Small loop low-bingo
Doesnt matter if you load snares or not,when they go right thru without touching the snare.-In the snow the greenhorns call them ghosts.The animal doesnt even break stride and slink right thry without a hair touching the loop'
I learned my snaring from the big numbers snaremen on the line,in this area and there were,are plenty of them

I wouldn't change a thing Boco if its working for you, but these are the typical results for me....

Big loop,low-lots of Ghosts. lots of hip catches and knocked down due them climbing over it
Big loop high-lots of misses-knocked down snares catches fur perfectly right around the neck
Small loop too high they go under they miss to the side too often
Small loop low- bingo they go over or step through, maybe catch by foot if you didn't have a deer stop

Doesnt matter if you load snares or not,when they go right thru without touching the snare.-In the snow the greenhorns call them ghosts.The animal doesnt even break stride and slink right thry without a hair touching the loop' - true but you need to set them so high they hit just under the chin. For Fox as an example that is 8-10" off the walking surface.

I learned my snaring from the big numbers snaremen on the line,in this area and there were,are plenty of them - I learned from a huge myriad of snaremen, and the school of hard knocks over the past 35 years I have been snaring.

I don't know if I ever snared a coyote that wasn't around the neck and if I ever did catch a fox that way its been 25+ years ago. Those are all I snare these days. My boy snares the beavers these days and the only ones of those he catches that aren't around the neck are the very few kits he catches.

You wont catch anything here, fox wolves or cats with the snares too high.
They come in to the jackpot very low.All you will get is knocked down snares,and if set correct height(low) but too big a loop -ghost animals or flanked catch.
Like I said trailsnares set higher,because animals are walking looking ahead with head a bit higher except canines on occasion when walking the trail will drop their nose down. I still use a small loop for trailsnares for a high carotid lock up.I dont want the loop hitting them on the chest,especially on wolves-it just doesnt kill them quick enough and you will get chew out,Trailsnares pale in the catch rate to jackpots so very few trailsnares are set,only on the rare occasion if it presents itself.I got away from creating trailsnare sets years ago in liu of jackpot snaring.
The small loop is key when snaring for quick humane dispatch with the snare locked up under the jaw and right behind the ears.You just dont get that when the loop is too big and triggered by the chest with low on the neck lock up.
I started snaring around 1965 when I was 9.

Changing goal posts here

Snaring bait stations or lured snares is a randoml thing.

How you rack up numbers snaring.
Really a waste of time snaring any other way in winter.I learned long ago to bring the animals in not waste time and effort chasing them around.
So I say set how you like ,but dont be scared to try new methods and then you can tweak your setting to be more efficient,effective and humane.

Can't run exposed carcass baits or set within x amount of yards of an exposed bait in many states.

Dont have to be exposed to work just fine.
Lots of trappers use a buried dead pit with vent hole.
Activate after freeze up.

Most are not going to bury baits. When freeze up happens trapping is shut down largely here. When we do use baited situations, we have so many snares out they will hit standard trail sets at the higher loops. Go much farther south of me and it almost never freezes up and there's so many gut piles and unrecovered deer that bait stations aren't all that effective. And when it does get that cold, we're running into breeding season which also kills effectiveness unless it's been a real cold winter.

Low loops also bring leg snaring deer much more into the situation. That's why when I ran coon snares those were always in either thick cover or had deer stops on them because theithr perfect size and height for a deers leg caught.

Who cares what you do there-The trapping world doesnt revolve around your bubble.My information is for snaremen in other places that trap throughout the winter.
A loop 6 inches off the ground or 8 wont make a lick of difference if you set where deer(or moose where we are) use(which is dumb) but makes a huge difference in catch rate for canines or cats.Same with a wolf snare set 8 inches off the ground or 14 wont make a difference to a mosse if you are dumb enough to set where moose are.

When you bring the animals to you instead of chasing them around you can set up where Non targets like deer and moose will never be an issue.