You could put a dehumidifier in the space. A dehumidifier is basically a refrigeration unit which is optimized to condense water vapor from a space. It will not cool the space and in fact will be a net heat source.
There would be a problem in getting rid of the condensed water. You would want to pipe it outside and have it drip into the ground. Some dehumidifiers empty into a reservoir which has to be emptied by hand which would not be desirable. Some dehumidifiers poder have a pump to allow the water to be piped away and even raised to get it out of a basement.
EDITAR
If you added an outlet or outlets from an a/c duct passing through the crawl space to direct conditioned air into the crawl space, this would be transporting air from the living space into the crawl space. The net loss of air in the living space would create a slight negative pressure in the living space relative to the outside and cause infiltration of outside air into the living space.
So you would need an air return to allow the air from the crawl space to get back to the air handler. This would basically connect the crawl space to the living space. You should carefully consider this before hacking into the ducting in the crawl space.
It may be that since you have a concrete floor in the crawl space you could get just enough air flow into and out of the crawl space to keep it dry enough for storage. The register on the vent could be adjusted so the air flow would be just enough to accomplish what you want, but I think you should obtain professional opinions on whether this actually works in practice.