The company I worked for provided two kinds, experimenting as they went along.
The first kind of cooling vest they tried used circulating air, using an air hose attached to a fitting on the side of the vest. However, the fitting became
very hot and would burn you if you accidentally brushed against it. This kind of vest worked reasonably well, but the obvious limitation was you were tethered to a length of hose attached to supplied air (NOT oxygen, the plant at which I worked piped plain 'ol air throughout the facility for various purposes). Obviously this kind of cooling vest is not practicable for your needs!
The second kind they tried looked like a Type III PFD (life vest) with pockets all around into which giant frozen ice packs were inserted. These worked well, with the ice packs remaining frozen for several hours despite the extremely hot and humid working conditions in which they were used!
The examples I listed are, perhaps, too extreme for your purposes. I wore the vest underneath a protective PVC acid suit, as seen here
while working on the steel deck of a ship in 100°+ Houston weather. All I can say is I lasted a lot longer with the vest than without it!
On edit: I would highly recommend an ice-pack type cooling vest - if it can stand up to the conditions in which I wore one, it would more than serve your needs.
The only down side I can see is you would look like you are going boating - you would be really cool (literally), though!