In my experience, the choice between "no woman" and "no women" is usually determined by this question: if there were at least one woman, would there be only one, or multiple?
This list identified sixty-seven men and no women.
We use "no women" because if the list did identify at least one woman, it would probably identify multiple women.
No! I'm not married! I'm a single man! I am married to no woman!
We use "no woman" here because if the man were married, he would probably be married to only one woman.
We have lots of hot dog buns, but no hot dogs.
We use "no hot dogs" because if we did have at least one hot dog, we would probably have multiple hot dogs.
I own a computer, but no TV.
We use "no TV" because if I did own a TV, I would probably own only one TV.