That's exactly the same thing I face as a performer. When the nerves get going, the fine muscles in the hands don't respond properly. So much of violin technique is in the subtleties, particularly the bowing, and when my nerves kick in, I get a bit shaky. That ends up completely destroying my tone. The bananas really helped to settle that shaking. I still wasn't as calm as I would be at home practicing, but it was a notable difference.
I've found trying to talk myself down does no good, because my nerves don't kick in until the very last second, usually as I'm tuning, right before playing. Same thing happens at the dentist...