A (1950s?) book about a later solution inventor (possibly a Henry Kuttner collection)

I’ve hunted for years and have still yet to recapture the author’s name or title of this short story collection. I am trying to recall the details as best as my memory – forty-plus years later – tries to bring them back.

It is a collection of a dozen or two SF stories from somewhere in the 1930s to 1950s probably; it was in a tattered paperback in my local small town library in the mid-1970s. (In Canada, so it could have been British SF, but likely American.)

All the stories were about a scientist / inventor who was slightly bent. He would be called on to come up with something and the solution he came up with would fit the request made of him, but it would ironically undermine the original request, similar to the resolutions of Isaac Asimov’s Azazel stories. For example, and this is the short story I remember most clearly, the military has come to the scientist / inventor to create an army to replace human soldiers. He does this by creating an army of human-sized rabbit-like clones/creatures, but the twist of the story is that all the rabbits are female and therefore unable to be drafted and serve as soldiers. Six- or seven-year-old me just laughed and laughed at this. The rest of the collection is like that, but this was the one I laughed at, small, naive child that I was.

Over the years when I’ve described this story and this story collection, people have pointed me to Frederic Brown and Henry Kuttner, but I’ve read through their books and, for the life of me, I can’t find this story among them.
This strike any bells with anyone?