Maybe we are a bit off topic, but here some remarks.

Radiactive Isotopes from nukes can be found everywhere on earth. That is true. However, this 'fallout' integrates all nukes ever exploded. The ones used in WW2 were rather small. Additionally you have to see where the bomb explodes, on earth, below or in the atmosphere. The inpact on the radioactive material is very different.

The worst thing of nukes (at least on a global scale) is not the radioactivity, it is the dust in the atmosphere that darkens the sky. If memory serves it takes some hundred years until it falls out again (experience comes mainly from volcanos).