Swamp coolers only work well in desert air where the humidity is very low. They depend on evaporation to work and when the humidity is already high, like here, they don't do much except add rust to your tools.
Is your shop insulated? That's a needed first step. Then for that much space a 2-3 ton or more air conditioner, depending on how well you insulate, is going to be required. A heat pump would be better because it could also heat your shop in the Winter, and because there are no very high temperatures created by it your shop will be much more fire safe than many other methods of heating your shop. When air conditioning, you are also removing moisture from the air, which reduces the rust problems as well as make you more comfortable. However, if you open a garage door for even just a few minutes, you loose your nice cooled air and replace it with hot humid air. It will take hours for your air conditioner/heat pump to get things back to normal again. Welcome to the Southeast.
My shop is about 1/2 the size of yours. It is insulated 3 1/2 in the walls and 6" in the ceiling. I have a 24,000 btu (2 ton) heat pump high on the North wall of the shop that maintains comfortable conditions in my shop all year. I do my best to never open the big doors and my rust problems are almost non existent. My shop is about 80' from a lake and only about 5' above it too. Lots of ground fog when the water is warm and the air cool.
Charley