Okay, I think I'm the best judge of what The Edge is most likely feeling. I'm 22 and have been losing my hair for the last few years. (Yeah, it sucks, but it really isn't that big of a deal).
It's true that almost all men feel shocked and embarassed when they START losing their hair, but after they accept it life goes back to normal. The Edge has been bald/balding for over 15 years, so I think he's okay with his lack of a mane. My opinion on why he continues to wear beanies or caps relates to his job. As a rock star, he feels the need to 'look' the part. Typically, rock stars are youthful and exhibit physical traits of the youth culture. Being bald isn't a sign of youth, but rather a sign of maturation and wisdom. U2 knows this, and until they attempt to win an older crowd, and give up on the TRL crowd, The Edge will continue to conceal his baldness with a cap, and Bono will continue conceal his wrinkles and hairloss with a pair of glasses and hairplugs.
At least the Edge isn't wearing a toupee or getting implants like Bono.
I'd like to encourage Bono to let go of the hair products and bald gracefully. I always thought he's be "above" the rest when it came to aging, but apparently he's more mortal than I thought. I should be laughing at that statement, but sadly I'm straightfaced (LOL). Okay, I laughed! But that doesn't erase my disappointment.