"...sounds a little crazy..." Yep. Especially as dynamite is far too stable to be set off with a bullet. Except in movies.
What kind of range facilities do you have? I'm guessing there may not be a formal range, but lots of space to set one up? Can you have paper targets printed? Got materials to make target holders?
Got a bowling alley? Old bowling pins make dandy targets. (You might be able to get the bowling alley owner to donate them.) Knock 5 over in the fastest time and you win. Down here there are lots of specialized timers used in assorted matches, but a regular stop watch will do. The only thing is pins are wood and will get shot to pieces quickly by shooters using regular hunting rifles. The biggest advantage of pins is that something happens when one gets hit. Makes it fun for spectators too.
Another idea would be paper targets, say a square foot, with a grid having random numbers in the squares, at 100 yards, using any rifle, any sight. Turkey shoot targets. Charge a nominal fee per target. Five shots only, highest score wins. A grid line that gets touched by a bullet counts as both numbers. You're shooting at a piece of paper that you can't see the numbers on. Even with a scoped rifle won't help much.
Don't know if it's possible, up there, but there's no feeling better than bringing home a turkey or whatever. I can still see the look on my ma's face the first time I did(my da brought one home every year from his bowling league). Maybe cash for the adult shooters and some kind of food for under 16 shooters? Mind you, I don't know any under 16 year old that wouldn't be exstatic winning $500. Not many adults either. I would suggest prizes for adults and prizes for younger, less experienced shooters though. Ask the other local businessmen for a donation. The worst they can say is no.
And a hearty well done and welcome to the site to you. You have to tell us all how it goes too.