Look around at flea markets and antique stores for the German military metal gun oil bottles. The bottle is unfinished metal with no markings. I have seen them everywhere. The German government must have made a ga-jillion of them. They are round, about 2 to 3 inches in diameter and have two separate compartments. Each compartment has a screw top. I know oil was kept in one compartment and I guess a gun cleaner of some kind was kept in the other. When you get one, you usually have to use something like kerosene or mineral spirits to soak out the congealed oil that was in them when they were put into storage. But, once clean, you can put your Moose Milk in one side and your favorite bore cleaner in the other side. It is small enough to easily fit into your pocket or possibles bag. In use, you would open the Moose Milk side, put the patch over the opening and tip the bottle over to wet the patch. Replace the cap and then squeeze out the excess Moose Milk between your fingers. Bingo! A damp patch ready to do its job in your rifle's bore.
If you can find a reproduction of a Yankee Civil War leather cap box that fits on a belt, the German oil bottle fits nicely in it and you can carry it on your belt.