The smaller sizes are fitted differently. I have three size 34 peacoats. The p2p on all of them is a steady 19", so the normal rules aren't followed in the smaller sizes. A size 36 has a p2p of about 19.5" to 19.75"
Rather than a droopy shoulder, it appears you may have a bit of scoliosis going on, which causes you to stand a little crooked and, as a result, the shoulder hangs a little lower.
I would have the sleeves lengthened as, in my opinion, they are just a little short.
Most post war size 34 peacoats measure19" p2p. I imagine the WWII coats are just a bit smaller. It ought to be a decent fit in the chest, but the body length and sleeve length probably be too short. My wife is 5'4" at 118 lbs. She wears a size 34 peacoat. It is a little large on her, but she can wear it OK.
Peacoats are double breasted garments and not particularly warm for Canadian winters. You might do better with a Filson Double Mackinaw. It has two layers of insulation (100% virgin wool) over the shoulders and yoke for climates such as yours. Their standard Mackinaw has a single layer, and is less expensive. They are waterproof enough to keep the snow off. The length is given as 31" compared to a peacoat at 32" in a size 42. I don't own one, but have heard others...
I have seen, and measured, size 34 coats from the the seventies and eighties only (there may have been a sixties in there, as well). These all measured 19" p2p. An odd anomaly. I would think (an educated guess) that the WWII coats are sized about the same, but perhaps a little smaller than the post war models.
Normally, size 36 and below have p2p that are different from the larger sizes. Most (all?) of the size 34s I have seen have a p2p of about 19". The size 36s are about 20". These p2p measurements are a little larger than we would expect based on our experience with the larger sizes--38 and above.
Is the seller, the one who said that was 1/8" to 1/4", a woman? I'm betting so. What I am seeing is the standard amount of material typically available inside the cuff of a peacoat. There should be more under the lining. You will be able to get at least an inch out of that, and maybe a little more.
Also, I'm betting the p2p measurement is off as well. Probably closer to 20.25" than 21.50", which was furnished by the seller. She probably didn't measure correctly.
If there is only 1/4" of material at the cuff, you are out of luck, as you will need sleeves longer than 24". Often, though, there is additional material under the lining at the cuff. A tailor or a seamstress can attach a piece of material, called a bias to get the most of what original material is left.
In most of the peacoats I have seen there is sufficient material inside the cuff to lengthen the sleeves about an inch, perhaps a little more. It would be unusual to...