Naturally occurring Uranium is about 99.3% U-238 and 0.07% U-235. Natural Uranium is processed (enriched) to separate as much of the fissile U-235 as possible for use in reactors and nuclear bombs. What is left over is uranium that has been depleted of its U-235. Depleted uranium is comprised almost entirely of U-238. No radiation hazard at all. Wouldn't want to be shot at with a depleted uranium projectile, but you won't grow a third eye due to radiation.
The health issues in Hiroshima and Nagasaki after the detonation of the atomic bombs were far more likely to be from exposure to the massive X-ray flash from the bomb's detonation and not from residual uranium or fallout. Anyone close enough to ground zero would have simply been vaporized by the X-ray pulse. Those farther away who managed to survive the X-ray flash, thermal pulse, shock wave, fires, etc. could have received X-ray doses which could have been lethal in a few hours or decades.