OK, I was listening to an episode of the Bickersons, which is an old time radio show, about a couple that constantly bickers.
Anyway, Mr Bickerson is complaining about Blanche (his wife) constantly wasting money. He says, “you bought a bald mink coat…”
OK, now is this a real thing? Or is it just a joke? This is an old time radio show from the late 40s.
If it is a real thing, what exactly is it?
It’s a joke. There is no such thing (at least intentionally). Four of the five Google hits are for that Bickerson’s episode, and the other is also a derogatory reference to a poor-quality mink coat.
A joke. Buying a bald mink coat (one without the fur, just the skin), would be a waste of money.
Really? People buy bald cow coats all the time.
As previously noted: it’s a joke. The reason one purchases a mink coat is for the fur (not the skin, curious11), so a bald mink coat would be an epic waste of money.
While I’m sure you can’t be serious, there is a obvious difference in quality between mink fur and cow hair.
People use cow hide to make leather because it’s thick and durable, and the hair is coarse. It would be absurd to use thin mink hide for leather.
[Father Mulcahy] Is that The Bickersons? I love them![/Father Mulcahy] 
I figured it was a joke, but it was during the 40s and I know because of the war they had a lot of substitutes because things weren’t made. So plain things were often called by other names to make them sound fancy.
If it makes you feel better, my first thought was “bald” as in “white” (bald eagle, bald-faced hornet, etc).
The family of my best friend growing up had a couch with non bald cow covers. It was an itchy couch to sit on. Eventually the cow fur wore away where people sat and the couch was nice to sit on.
My first thought would be: he bought a mink coat so old/ damaged that all the fur had fallen out and therefore, it had become a “bald” coat - showing its cheapness compared to a real mink coat with fur.