My job as a professor depends on public speaking, and as much as four hours a day. Since my sweating is worst on my torso, I have bought sutran undershirts (designed for one suffering from compensatory sweating as a result of ETS), and these make it virtually impossible for the sweat to seep through the clothes, even when I feel it gently dribbling down my back and stomach, a truly delightful feeling. The only downside to these: these shirts are so thick and snug that you feel much warmer as a result. But it's a worthy trade-off for several hours in front of a class or conference audience.
Nerves don't typically kick off the sweating for me. An overheated, overcrowded room with no air circulating will, however, particularly if I expend a lot of energy in a futile effort to keep people awake. Most of the time, I'm able to get to the classroom well before the start of class and crank up the a.c.. In the winter, I open the windows. So far, I don't think anyone has noticed a thing, even if I am constantly aware of it.
The reality is that most people's attention spans are short. Most, depending on the time and circumstance, are probably going to be thinking of something a lot more exciting and important to them than us and our sweating. We hold ourselves up to the mirror, but they may not notice a thing. And if they do, they may not even care all that much. Worst case: explain that you have a medical condition (without giving out many details), but one that is not going to make you drop over and die.
