Aren't primers and powder shipped HazMat, but loaded ammo shipped regular?
In a fire, loaded ammo bursts (not explodes) when the propellant (not explosive) reaches ignition temperature. Unless contained within something like a barrel or a revolver chamber, there is almost always so little "oommph", the case will not go fast enough to pierce a cardboard box.
Powder and ammo are "explosive" only when subjected to adiabatic shock--i.e. another EXPLOSION!
Primers are another matter, but in original containers and assembled in cartridge cases, the explosives act in isolation and are too small to be a regulatory concern. Your eyeballs and the first 3mm of your skin are the only things in danger when a single primer lets go.
Do NOT believe what you saw in "Rambo." The gunstore explosions were PURE fiction. It takes a warehouse full of smokeless powder, or a huge pile of black powder, to blow up.
Black powder *is* a low explosive, so you probably can't do the muzzle-loader thing at your new Apt.
Get a copy of the Uniform Fire Code or your local county fire code, and look up the gunpowder storage regulations. Comply with them. Note that they call smokeless powder extremely flammable or something like that. Explosive release of accumulated burn gas pressure is possible, but only if the stuff is improperly stored. The container explodes, not the powder.