I don't know, not being a nuclear weapons expert, but publicly available discussions of triggers for plutonium bombs describe mixing polonium (an alpha emitter) with beryllium to produce a neutron source: when beryllium nuclei of the appropriate isotope are hit by energetic alpha particles, the shed a neutron of low enough energy to be captured by plutonium nuclei.
If the polonium and beryllium are mixed in advance, the neutron emission is wasted, so the mechanism must be able to mix polonium with beryllium during the detonation sequence, suggesting that the two compounds would be finely powdered in the trigger.
Inhaled, licked fingers, had a bit fall out of his pocket or cuff onto his sushi, who knows?
Polonium-210 is a low-melting, fairly volatile metal, 50% of which is vaporized in air in 45 hours at 55C.
Perhaps enough of it vaporized at room temperature that he received a lethal dose just from inhaling.
The idea that this was a Putin hit job is looking less credible.