Tues Nazir 59

The Gemara forbids someone to shave his armpit hair. He cannot have an excuse that it's uncomfortable, since it doesn't grow that long.

Tosfos proves that we forbid even trimming the armpits with scissors. If it would be permitted, even if the armpit grows very long, you won't have an excuse to shave it with a razor, since you can relieve yourself with scissors.

Also, it implies that if there was a valid excuse, you can cut the armpit hair as long as you don't do it for beauty. Thus you can look in the mirror (even if generally you consider that to be a woman's activity) to avoid hurting yourself when you shave.