That can be circumvented with careful preparation for transport and the like. Its done in reality too.
The difference I think should be as follows;
-Colliers are built to store missiles, so do it in a much volume-effective way. The missiles loaded onto a collier are also fully functional, and thus can be used to resupply another ship in space.
-Cargo ships can move missiles, but these need to be partially disassembled and packaged which takes a lot more space than on a collier. It also means that a cargo ship can only unload the missiles at a colony where they are reassembled for use (perhaps requiring a spaceport or something to signify this).
In other words, Cargo ships can do the logistics role as part of your supply chain, but for fleet operations (or more efficient transfers) you need a collier.
Since someone draw a War in the Pacific parallel, the comparison there is an xAK/AK, and an AE. One is purely for moving 'stuff' (including ammo), the other is what you need if you actually want to resupply elsewhere than at a port.