No, the whole "releasing toxins by sweating" is a myth. There are only trace amounts of toxins and it doesn't really make a difference in that regard. It's just a way to cool down.
In general you are right that sweat cools down your body. But were you have hair (pubic, armpit) the sweat does not mainly cool you down (evaporation from hair doesn't cool; this has to happen on the skin) but carries chemical messengers like pheromones( the hair provides a larger surface ta adhere to build up more aroma volume).
So shaving and using all kinds of spray suppresses interpersonal communication(like fear, ovulation, arousal) what is kind of bad.
The actual stinky part about sweat are microbes living on your skin processing your sweat into something stinky.
So if you do not want to suppress the chemical messengers and you do not want to stink you can use something called cristal deo( at least in germany). It only stops the microorganisms to do their job.
So back on topic: when the girls do not shave their armpit you are more likely to find their horny days or find the one horny girl in the room.