Archie Goodwin and Nero Wolfe have been solving crimes in New York City for ten years (by the dates of the books) and have got a reputation for it. So when Archie, who serves as Nero Wolfe's right-hand man, volunteers for the Army, he's not sent overseas, but is assigned to Army Intelligence, where his main task is to prod Nero Wolfe into working.
Well, if you know the series, that's generally the first task in any book.
Not Quite Dead Enough contains two novellas, the title novella and 'Booby Trap.' The first finds the normally (and still) corpulent Wolfe, dining on prunes and lettuce, forswearing beer, and exercising, until he can get in shape to join the Army as an enlisted man and go overseas. But that's not what the Army wants him for: they need him for some unspecified mission, and they need him in his role as the thinking detective. Archie gets him back to working, and that's the majority (and especially fun part) of the story.
The second novella does involve war issues, though it still takes place in New York; Captain Cross is dead under suspicious circumstances; threatening letters appear; then Colonel Ryder is killed by an experimental grenade. Murders? Well, yes and yes. And Inspector Cramer of New York Homicide can't (as usual) solve them, but this time because the relevant information is classified.
I thought the first novella better than the second, though if I were recommending a place to start with the Nero Wolfe series this book as a whole would not be it. If you like Wolfe, though, you won't be disappointed. I wasn't.
Rex Stout was 55 when the US entered the war, and according to the introduction, spent the war years chairing a variety of committees, hosting radio programs, and otherwise engaged in war work. But still found time for a couple of novellas.