I suppose the vapor pressure could be lower than that for water, if there were effectively none in the air already. That would only be more effective than sweat on very humid days. You would be wetting your wet bulb with two different liquids.

The trick is to find one better than water that is also non-toxic, non-flammable, non-carcinogenic, and non-polluting. It would almost be easier to just remove all that water from the surrounding humid air, so that sweating works to cool you down again....

The phase-change material between liquid and solid would work better, but still requires a separate cooling technology to "recharge" it. And phase-change material still works better in building walls than in clothing. So you're right back to keeping your whole building cool, rather than a specific person.

You could also strap a personal radiator to your back, but no one wants to work on the tropical plantation in the first place, much less do it inside spacesuit-like apparel.