Two pieces of advice that I think work.
1. Always scare yourself snowboarding at least once a day it's how you progress as a rider.
2. People that are afraid they're going to get hurt, tend to be the ones that get hurt because they're afraid they're going to get hurt/can't do this so they bail.
Yeah, my comment isn't so much park related, but I tell my GF and all my buddies that get into riding to learn to live with falling because it's part of snowboarding. I wipeout everyday in the offpiste...
If you're not falling, you're not trying hard enough in my books. Then you're just a tourist.
Best thing to do when you fall, laugh at yourself.
Also, if I'm about to plunge off something that gets my heart rate up, I'll take a few deep breaths to oxygenate my blood. Calms me down and sets me up for the run/jump/chute/whatever.