Half joking. Is the material and spatial separation of a lab coat enough to prevent a reaction between two lumps of plutonium of sufficient combined critical mass? It might be since it's so bad at penetrating anything solid, but I don't know.
It's still a horrifyingly unsafe thing to do.
https://en.wikipedia.org/wiki/Demon_core#/media/File:Ticklin...
https://www.science.org/content/article/near-disaster-federa...
This isn't the case!
Plutonium 239 is relatively safe, merely an alpha emitter which is what you're talking about. But that isn't where the danger comes from. The danger comes from the Plutonium 240, which is present as a contaminant in all plutonium weapons cores. Plutonium 240 spontaneously undergoes fission, releasing neutron radiation which is very penetrating. If you bring two halves of a core together, neutrons from the spontaneous fusion of Pu-240 can cause a chain reaction; this is the reason gun-type bombs don't work with Plutonium cores; they give off too much neutron radiation and would react prematurely if you tried to build a Plutonium bomb like that.
Inverse-square law [0][1] applies...
[0] https://en.wikipedia.org/wiki/Inverse-square_law
[1] https://energyeducation.ca/encyclopedia/Inverse_square_law
One of the things modern "computing practices" taught us is the myriad of ways things can go wrong, they were probably a bit more naive at that time
It's Murphy's law squared