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Lead is needed to shield against the gamma radiation (high energy light, like hard x-rays). The heavy alpha particles (much more damaging if exposed) are readily stopped by even modest amounts of just about any solid material (as are the light betas particles, which are just fast moving electrons). U-238 is radioactive yes, but not that much, certainly not compared e.g. to plutonium. You wouldn't want to be exposed to a lot of it completely unshielded, certainly. But you block ~95% of the danger with even thin shielding.

15.7 kg of U-238 would have been 66 mols or 4x10^25 atoms. (238 grams per mol, 6x10^23 atoms in a mol). The half life of U-238 is 1.4x10^17 seconds (4.5 billion years), so you get roughly 3x10^8 Bq for the triggering top of the decay series (300 million atoms per second). That is less than the radioactivity from 1 gram of plutonium (2 billion atoms per second). Throw in the subsequent decays down the chain, and it would probably be comparably to a gram or so of plutonium. If enriched (some U-235, lower half-life, faster reaction), naturally the rate would be somewhat higher. The small amount of U-235 in natural uranium contributes around 10% more; purified U-235 would be an order of magnitude higher than U-238.

In short, uranium is not like plutonium, or like half or a quarter as much plutonium. It is thousands of times less radioactive, so kilos of it are like very small amounts of plutonium. Most nuclear weapons use plutonium triggers; it is much more efficient. They require some shielding of course, but are readily handled with such shielding, when building, transporting, or servicing the weapons.

So it was perfectly plausible that there might be 15.7 kg of uranium - though probably not truely weapons grade uranium (meaning 90% U-235). It would hardly be impossible to transport, it would not blow up or act like the fantasy cargo in a Repo Man car trunk. When I saw the report, I was skeptical they had 15.7 kg of 90% U-235, but considered it about equally likely they had 15.7 kg of uranium (just something like 3% U-235, 97% U-238) or that they had 700 grams of U-235 in 15 kg of package and shielding. It now appears from the corrected reports that something like the latter is the case.

Lead is needed to shield against the gamma radiation (high energy light, like hard x-rays).

Actually, lead is choice ONLY if the photon is very low energy
such as below ~100 keV (the photoelectric region)
where absorption goes as Z to 4th power.

If the gamma ray is in the range of 100 keV to 1 Mev
(the Compton region), the absorption is not even a function of
atomic number, so concrete works as well as lead.

Above ~1 MeV, the photoelectric region begins, absorption goes as Z.

And so it goes.

Thanks for the interesting walk through the calculations. It felt a bit like inorganic chemistry with a touch of particle physics :)

The explanation regarding plutonium vs. uranium is well taken. Part of these explanations are also relevant to deep-space exploration vehicles which require plutonium sources for an energy source. The environmentalists were concerned the launch of such spacecraft would kill everyone on Earth if the spacecraft crashed. They were using no calculations of the sort you just did.

My understanding is that there are several different separation techniques to refine the radioisotopes of uranium and that the Manhattan Project spent a good deal of effort on that step in the process. Wasn't a centrifuge separation technique used?