Cat Man has recently been written very well as part of the Secret Six (New 52), which is a pretty oddball team but their books have been great.
It’s not literally the 40’s character, but it pretty much is the same concept and I think an intentional homage. For a hand to hand person it turns out catlike agility is pretty great.
Unselfconscious, yes. But it’s like tormenting the punching-bag kid at school. You feel bad about it…but not bad enough to refrain. This is just like a schoolyard when you get right down to it. Everyone wants to assert their superiority…even when it comes to old-timey comic books.
There was an homage to that character in the first issue of one of revivals of the Justice Society. After Johnny Thunder’s funeral one of the characters says “At least there was a good turnout.” Another replies “Yeah. The only people at Madame Fatal’s were the touring cast of La Cage aux Folles.”
There were plenty of weird characters in the Sixties, especially in off-brand comics.
There was a Captain Marvel who was an android build by aliens. He could fly, had laser vision (I think) and - the big one - split his head and limbs from his torso.
There was also a comic about four teens who could transfer their minds into four matching (by sheer coincidence) androids. From a different company, probably a different creator.
Herbie Popnecker was mentioned by someone else, and is definitely worth looking at. He’s the greatest hero who has ever lived, and everyone knows him except the bad guys, the kids and teachers at school and his parents. He even romanced Jackie Kennedy and Elizabeth Taylor (as Cleopatra) and was pals with Khrushchev.
Nice selling point that it actually contains “full comic stories”. There’s been many a time that I’ve seen those lists of wacky out-of-context comic panels and dearly wished to know how they could possibly have made any more sense in context.