I have the impression a dirty bomb would be created using nuclear waste from nuclear energy generation (rather than especially formulated material) - which was actively being researched for commercial use at the beginning of the 40's by Argonne National Laboratory (according to wikipedia) - which to my mind means it was probably already being utilized by the military industrial complex in a non-commercial way, and then they would have access already to waste by the time they are doing test detonations...

You may say but then the radio-activty would be too weak... but then there is evidence that the radioactivity measured at Hiroshima and Nagasaki was very weak, or even non-existent.

shadows on a wall

It's one of those things thats so well known and such a striking visual of the nuclear detonation, without actually depicting detonation, that I wonder if those images depicting it were faked or perhaps even just caused by someone completely on fire falling against the wall. We are told they are shadows, but they are not sharp, clearly defined shadows, and they also look like they could be carbon soot on the wall in a vaguely human shape.

There were trees left standing at "ground zero" in Hiroshima and Nagasaki. The shadows in the images are left on concrete, the concrete was otherwise unscathed - not vaporized. There is a bridge directly under the detonation location, brick and mortar, still standing. Only the wooden structures burnt. The brick and mortar of the buildings remained standing, intact, just stripped of any wooden parts.

The Hiroshima and Nagasaki destruction doesn't look much different to the firebombing of Dresden, except that there were far more brick and mortar buildings in Dresden. Napalm dropped on buildings would burn away all the wooden ones (and wooden parts) which were the majority of the buildings in these fishing "cities" Hiroshima and Nagasaki.

A nuclear blast should be indiscriminate - it would vaporize all the wood, including the tress, not just the human structures made from wood. A Human directed firebombing campaign however, would target human structures and not necessarily be too concerned with burning down the trees that line the streets.

There is another book about Hiroshima and Nagasaki specifically which tackles the issue based on the medical evidence of effects on victims - Hiroshima Revisited

This book examines the scientific and medical evidence to determine whether the conventional story of the atomic bombings of Hiroshima and Nagasaki can be true. It concludes that

1. no nuclear detonations took place,

2. the cities were destroyed with conventional explosives and napalm,

3. the victims were killed not with radiation but with mustard gas, and also with napalm.

While most of the book deals with the medical and the physical evidence, the final two chapters also examine the wider historic and political implications.

That author believes real nukes were developed later, so it disagrees on that with the other book I've linked to.