This is a fun little event that can be part of a larger event, such as a fair or flea market. 

Find someone in your circle of acquaintances (preferably someone well-known in the community) who's known for his moustache or beard (or both) AND who'd be willing - though certainly not happy - to allow it to be shaved off IN PUBLIC. 

Days or weeks before the big Shave-Off, solicit people or organizations to sponsor the humiliating event.   Only those who've donated would be allowed to witness the spectacle.  Make a big deal of it, enlisting the services of a local barber, maybe someone with a flair for acting. 

Set up donations/sponsorship areas before and during your bigger event, featuring a large flyer with the victim's photo and captions such as "Have you EVER seen (Joe Barker's) face!  Be among the first in this century to ....."  You get the idea.

Try variations on the theme.  A woman known for her long, long hair?  A man willing to dress up like a stripper. 

You'll need to bring your organization into the picture.  Don't forget to include your logo, address, etc., on every promo you put out, including the flyers.  Take pictures of the "victims" with shelter animals.  A dog licking the victim's face would be cute.  Feature that, after the shave-off, in the local paper.  Sell the picture to make even more money!

The more I think about this one, the better it gets.
Shave Off