According to the Oxford English Dictionary, the term means exactly what you'd think it means, and dates back to at least 1607. A woman-hater is:

"A person who hates women; a misogynist"

Some literature around the time of the World Wars suggests that it might have had a slight connotation as a man who abuses women, though this does not seem at all to be a universal meaning of the term. "Misogynist" would be the more appropriate synonym. And "misogynist" literally translates from the ancient Greek as "woman hater" so it's right on the nose.

A 1905 cartoon among others also slightly insinuates it may have sometimes been used in reference to a "confirmed bachelor", itself a euphemism for a gay man, but I wouldn't read that at all as a universal meaning, either. Again, it seems "misogynist" is the more synonymous term. The caption of the cartoon:

"Peck is a confirmed woman hater."

"A cranky old bachelor, eh?"

"Oh, no! He's married."

This 1922 slang-filled piece might give the best example of what its meaning would have been understood as in the 1940s. The term is used alongside a "caveman", a brute, a man who doesn't like women and doesn't treat them well. The man also seems to be attempting to attract women by putting them down ("negging" in the modern parlance).

In the article, the woman telling the story says there are three main types of skirt-chasing men in the city. The first type are the "Lonesome Guys" who just want to "dash around a bit". The second type are the "Fireside Flivvers" who are already married, but are looking for a "fliv", which essentially means a side-piece, to use the more modern parlance. And the third type:

"Well, No. 3 is the wildcat of the outfit and he had broke more manicures' hearts than Valentino. He is the guy who hates women. Zooks, how he loathes the fair sect. And he lets you know it the first time he sits in for a trim. If you throw him a Gloria Swanson right in the eye, he comes back quick: 'No use, girlie, I hate women. Gosh! How I hate women. They make me ill.'

"Well, this bird who just gets out of my chair is a woman hater and one of the worst cavemen I have ever met. As for me, I let him go on hating 'em for three or four weeks until he got calmed down to where he could talk about something else...

"Well, I refuse him seven or eight times before we get to Seventy-second street, but he still comes back for more, so I finally tell him no, I will not marry no woman hater like him and no caveman neither and that is final.

"'I'm no woman hater,' he says with a shaky voice. 'was only fooling. I don't hate 'em. I love 'em. I'm no caveman, honest to'—

"'Aw, be yourself and don't spoil my dinner,' I says and by that time we have reached this inn and have sat down and named the poison.

"'I ain't no woman hater, honest,' he says, lookin' at me across the table like a dyin' calf in the moonlight.

"'Maybe you ain't a woman hater now,' I says, 'but you soon will be.' And them is truthful words as ever was spoken."

Closer to the time of the Daffy Duck cartoon, is a review in the Washington Evening Star on May 2, 1943. The review is of the book Masterson by Lee Wichelns that includes the description:

"Mr. Wichelns tells the story of Masterson, raised in the slums, jilted by the girl he loves, a woman-hater who falls in love with a little schooner..."

Other examples in the era can be found in the Washington Evening Star on April 13, 1941, in the same paper on August 24, 1941, in the Carbon County News in Montana on April 17, 1942, and in the Enakopravnost newspaper in Cleveland on May 1, 1943. They all suggest the meaning of "misogynist".

In 1948, there was a British film starring Stewart Granger with the title Woman Hater. The IMDB description of the plot is:

"Terence is a bachelor who doesn't have much use for women. He meets Colette and takes a dislike to her. He pretends to be a real-estate agent trying to sell her his country estate, all the while planning to expose her."

The term "woman hater" seems to be often associated with the film industry of the era, in fact. There seemed to be many romantic comedies where a "woman hating" man at first resists some new woman in his life, only to be converted to a woman-lover by the end. Typical is this 1915 ad for the silent film The Girl and the Bachelor. Under the headline "Knows Ways To Win Woman Hater And Practices Them In Movie Play", the ad reads in part:

"In the picture Tom Moore is supposed to be a woman hater. Every time his mother tries to introduce him to a nice little miss, Tom makes a bee-line out of the house".

Unscientifically, by the number of hits returned on Elephind, it seems that the terms actually peaked in popularity closer to the 1890s-1910s, and seemed to be on its way out by the time of World War II.

For what it's worth, the term "woman hater" does not appear in any edition of Maitland's American Slang Dictionary first published in 1891, nor in Partridge's London-based A Dictionary Of Slang And Unconventional English first published in 1923, nor in Wood's Dictionary of American Slang published in 1926, nor in Flexner and Wentworth's Dictionary of American Slang first published in 1960. More contemporarily, it does not appear in Green's Dictionary of Slang, either.

It appears to be a term that means exactly what it seems to mean. Even if it was a term that was at one time used more often by the young, hip crowd than it was later used, it doesn't seem to be a particular euphemism for anything or slang for anything else. "Woman hater" means "misogynist" or a "person who hates women", and seemed to be more popular at a time when misogyny among unmarried, single men (and married men, too) was more acceptable and commonplace.

TL;DR: "Woman hater" means "woman hater", or "misogynist".