The easiest thing to do would probably be to deform the pit so it can't be used in a warhead without re-processing. Then store them in a box using the same policy/procedures as weapon storage. They don't take up a lot of space and it's not like they're being manufactured like crazy.

Wikipedia says they're about 10cm in diameter which sounds about right, i thought they were around the size of a softball. https://en.wikipedia.org/wiki/Pit_(nuclear_weapon)#Pit_shari...