Pu-239 is an alpha emitter, but that's not the end of the story. All plutonium weapon cores are also neutron emitters because all weapons grade plutonium is impure and contains 2-7% Pu-240. Pu-240 is very prone to undergoing spontaneous fission which emits neutrons. So the presence of neutron radiation around a plutonium weapon core is unavoidable.
Furthermore, when Pu-239 is struck by neutrons (from the Pu-240 contaminant, for instance), it has a chance of undergoing fission and that results in the release of more neutrons which can cause additional Pu-239 to undergo fission. This chain reaction is how Pu-239 bombs work. A properly stored core will not sustain this chain reaction because the core is in a sub-critical configuration.
So there is in fact a very serious critical mass concern with plutonium bomb cores.
Yes, alpha particles aren't relevant to the fission reaction, so the fact that it's easy to shield against alpha emission isn't relevant. It's all about the neutrons.
Furthermore, when Pu-239 is struck by neutrons (from the Pu-240 contaminant, for instance), it has a chance of undergoing fission and that results in the release of more neutrons which can cause additional Pu-239 to undergo fission. This chain reaction is how Pu-239 bombs work. A properly stored core will not sustain this chain reaction because the core is in a sub-critical configuration.
So there is in fact a very serious critical mass concern with plutonium bomb cores.