Saturday night I played an open mic at a coffee house with my Dad. We played 4 tunes,
You Can't Do That - the Beatles
Peter Pumpkin Head - XTC
We Can Work It Out - the Beatles
Everybody's Talkin' at me - Stephan Stills
I have to recommend doing this to every Worship/church musician. It is a totally different kind of nervousness. Sunday morning was a walk in the park. On Sunday, everyone is at least there for the same reason, with many of the same intentions about being in the same room. Saturday night in a Coffee House is a different atmosphere. Not everyone is listening, or cares too, but some people are genuinely interested. Anyway, the biggest difference (as it applies to your nervousness) is that no one is there to sing along with you, just to listen.
This is good for you/me in a few ways;
1) You get to hear just your own voice. A lot of things get lost in the live mix, the nuances of your voice, your inflections, your intonation. It's really good motivation to fix your singing problems when they are blaring back at you with just an acoustic guitar accompaniment.
2) Like I said before it's a different kind of nervousness. It is an actual performance rather than a worship experience, so you'll get more nervous. It's good, for me at least, to remember what that's like once in a while. I once read an interview with Ozzy (not that he's a great repository of wisdom) where he said "the day I stop getting nervous on stage is the day it stops being fun, and the day I quit" He probably actually said something that was much less understandable than that, but you get the idea.
3) You get the chance to connect with people in a different setting. I got to talk to other performers before and after our set, who told us what they liked about the songs, about my guitar playing, etc... Also you can see what kinds of songs people get into; Everybody liked 'You Can't Do That' because it's fun and we sing harmony and it's a classic. Fewer people got into Peter Pumpkin head; given it's a bit obscure and it's a re-telling of the story of Christ, so some people recognize that right away and stop listening, other people pick up on it and listen closer.
Anyway, if you're a worship leader you need to get out of your comfort zone and go play a few tunes in a coffee shop for the evangelism possibilities if nothing else.