In this story, humans have been destroyed (indirectly, their own doing) and all that's left are their machines, along with some stray animals and decaying plant life. So, another way to state the title would be to say "August 2026: There Will Come Mechanization" or "August 2026: There Will Come Self-Destruction" since humans are largely responsible for their own destruction. A more stark way to put the title would be to say "August 2026: One House Left Standing" or "There Will Come a Radioactive Glow" - both lines coming from the beginning paragraphs of the story.
Another way to go is to stick with Sara Teasdale's poem but use another line: "Not One Will Know of the War" - as if to say no animals, plants, or the seasons themselves will miss humans after a great war.
But perhaps an even better way to describe the tone, in the title or just in general, is to describe what remains of the humans themselves: white shadows or silhouettes which show where the family was when the bomb incinerated everything around them:
The entire west face of the house was black, save for five places. Here the silhouette in paint of a man mowing a lawn. Here, as in a photograph, a woman bent to pick flowers. Still farther over, their images burned on wood in one titanic instant, a small boy, hands flung into the air; higher up, the image of a thrown ball, and opposite him a girl, hands raised to catch a ball which never came down.
In this case, consider what is left: white shadows and silhouettes: "There Will Come White Shadows" or "There Will Remain Only Outlines."