Minimizing Humidity in Storage Shed

Vent the still outside.

setup to spray the water

ROTFLMAO!

With no electricity for mechanical cooling, id opt for a solar powered roof mounted Attic Fan on a humidistat ...with intake grilles low down on the walls near floor level.

I spent some time in the tropics and the darn windows in the huts on the Island of Pohnpei were nothing but screen wire so the sea breeze flowed through the dwelling. Question: At your location, is there a prevailing breeze that blows through the area? If the wind tends to blow in one direction you could use some sort of wind powered turbine vent up top with screened vents facing the prevailing breeze.

Cover the floor with a moisture impermeable membrane and store the wood off the floor, to allow circulation.

I built a firewood shed for my wife's house. It is open on three sides, has a very generous roof overhang and the wood is stored on 2X4 treated lumber, on edge (for strength) spaced on 1.5" centers. The wood stays dry - coastal NC - where humidity in summer averages 70% or so.

Put a turbine ventilator in the roof, a vapor barrier under the shed, vents in the building, down low.. (that you can close in the winter). If you can raise the shed so that there is a ventilated space under the shed, so much the better.

Don't store wet things in the building, let them dry first.