Can anyone tell whether these exposures occurred through the camera lens (from fallout particles in the sky of the depicted scenes) or in post- (or pre-) exposure handling of the film from hot dust carried by the photographer?

They are not part of the image of the scene. They wouldn't be focused by the optics.

The optics would just be a slight attenuation much like the rest of the camera housing, film reel, operator, etc. So really a summation of all the exposure types you can imagine.

There's no reason they would preferentially travel through the lens and hit the current frame because most of the camera and film housing is about as transparent to gamma radiation as glass. Or maybe more transparent, because glass lenses in pro cameras tend to be rather bulky.

So this just happened somewhere between arrival to and departure from the zone.