Can I cool my south facing wall by spraying it with water?
Evaporative cooling is less effective in places with high humidity. There are mathematic formulas for how much water will be needed to cool a specified surface area by some number of degrees and they are not simple. The wiki article on this has some good information. It would be good to get some idea how much water will be needed before heading down that road.  

Before I went that direction I'd look into something that is a one time cost vs. a recurring cost:


Planting trees to create shade.
Awnings - there are a variety of types. Some have the ability to retract and deploy based on the time of day.
Reflective coatings on windows
Vertical trellis (linked as an example, not an endorsement)
Painting the wall white, or a very light color.
Build a porch with a roof


Or some combination of the above.