There is no real respite from the heat/humidity in the tropics. If there is an antiperspirant that works in that kind of heat it would have to contain a very small air conditioner.
Shhhhh.....Don't tell anyone, but I hear on the bamboo telegraph that Tommy is really down there doing sweat gland conditioning for a trip to the surface of the sun (where it is fractionally hotter).

<<reference to the picture of Portobelo bay>>
"Headin' south to Paraguay
Where the gauchos sing and shout
Now he's stuck in Porto Bello
Since his money all ran out
So he hangs out with the sailors
Might and day they're raisin' hell
And his original destination's just another
Story that he loves to tell."