A few posts have touched on this matter, but I have made a point of seeking out old literature on the topic. Here are some excerpts:
Steel Traps (Harding 1907) says: RACCOON should be stretched open (ripped up the belly) and nailed on boards or the inside of a building. Some dealers allow as much for coon cased, from any section, while others prefer that only Southern coon be cased
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and This is my way of stretching coon hide; use four-penny nails and use either the inside or outside of some old building, inside is the best. Drive the first nail thru nose. This holds the hide for starting. Pull each forward leg up (not out) on a level with nose and about seven or eight inches from nose according to size of the coon. Drive next nail at root of tail, and pull down, moderately tight. Now pull each hind leg out about one inch wider than the fore legs and a little below the tail nail. Now use a nail every inch and pull the hide up between the forward legs and nose, until it comes straight across. Next, treat the bottom of the hide the same as the top. Use plenty of nails. To finish down the sides, drive a nail first on one side and then on the other until finished. You will find when done that the hide is nearly square with no legs sticking out the sides and no notches in the skin
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and Take two pieces of No. 9 fence wire about 30 inches long, writes an Ohio coon hunter and trapper, file one end sharp, then commence at each hind foot and punch the wire thru close to the edge as in sewing, taking stitches an inch or so long until you get to the front foot, then pull the hide along the wire just far enough so the top and bottom will stretch out to make it square, or a few inches longer than the width is better.Put 3 or 4 nails in each side, then commence at the top and tack all but the head, then pull the bottom down even with the sides, not tacking the head, which lets it draw down into the hide, then tack the head.This is an easy and good way to handle coon skins making them nearly square when stretched. Many inexperienced trappers stretch coon skins too long and draw out the head and neck. This can be avoided by following instructions given here. Coon can be cased but most dealers prefer to have them stretched open
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and Get a lot of steel wire, says a Missouri trapper who uses old umbrella wires, the round solid ones. Sharpen one end, take your coon skin and run one wire up each side and one across each end. In putting these wires in do it like the old woman knits, that is, wrap the hide around the wire and stick it thru about every inch. Now cut six small twigs, make them the proper length and notch the ends, and you will soon have your hide stretched expert trapper style. The advantage of this is you can carry stretchers enough for twenty-five skins in one hand and don't have to hunt up a barn door and box of tacks and hammer every time you want to stretch one. You can stretch in one-fourth the time it would take to tack up on a board, and you will have it in first class style the first time and not have to pull out a tack here and stretch a little more there
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and; The badger, beaver, bear, raccoon and wolf must always be skinned "open;" that is, ripped up the belly from vent to chin after the following manner: Cut across the hind legs as if to be "cased" and then rip up the belly. The skin can then be removed by flaying as in skinning a beef
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and The animals which should be skinned open are bear, beaver, raccoon, badger, timber wolf and wolverines. The way to do this is to rip the skin open from the point of the lower jaw, in a straight line, to the vent. Then rip it open on the back of the hind legs, and the inside of the front legs, and peel the skin carefully off the body.
Science of Trapping (Kreps 1909) says: The raccoon, bear, beaver, badger, cougar, wolf, wolverine and coyote should be skinned open. Some dealers prefer to have southern raccoons cased
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and The raccoon should be stretched nearly square and all other skins to their natural shape. A square frame is most convenient...
Raccoon, opossum, skunk, and weasel (Lenon 1946) says: Raccoon are skinned open and stretched nearly square, the body of the pelt is square with the head and tail exactly in the center and projecting out from the square part. To skin, split from the tip of the tail straight up the bell to the tip of the lower lip, then split from this cut straight out to each of the four feet.
Some various snippets to follow
Links to previous posts:
https://trapperman.com/forum/ubbthreads.php/topics/6487038/2https://trapperman.com/forum/ubbthreads.php/topics/7999607/square-stretch-raccoon-videohttps://trapperman.com/forum/ubbthreads.php/topics/7059876/stretching-raccoon-squarehttps://trapperman.com/forum/ubbthreads.php/topics/6473239/how-skin-coon-squarehttps://trapperman.com/forum/ubbthreads.php/topics/8013709/re-square-raccon