If theship being serviced is in destroyer size, the support ship would have to be around 1/8 - 1/4 of the ship, so almost as big as a cruiser. Actually this ship could carry enough conventional arnament for a whole regiment, so it would probably have a protection of its own.
The actual transfer could take place by opening up a part of the destroyer. The old container would be expelled on its own thrusters or with the help of construction/service craft (think of the crafts building the Colossus).
All what the service craft would have to do is drop the container, take the old one and jump out.
No prolonged transfer of cargo.
If you want smaller containers, then you could just carry them like another cargo container - with ordinary transports.
Loading is the same, with a smaller open partition and actual transports droping their weight.
The process could take several minutes, but at any given time only one transport and a single container are in danger - not to mention, that following the first transfer the destroyer already has a limited, but fearce battlepotential.
The whole open compartment thing would also help to protect the ship if an explosion takes place in the compartment, it can be dropped, so the ship can escape before it goes BOOM!
They would be a heavly armored, on their own, so the necessary armor is already there - in this case it's cheaper to go around with that much waste weight when the it's filled with extremely explosive stuff.
You can even go further, and make the whole changable compartment integrated with the laucher systen - you can change it whole.
Although I think this later system would work better with smaller craft, like bombers, where there's little space.
