I have sung on stage with a band in front of hundreds of people but wouldn't sing in front of anyone til I was probably 40?  I remember the first song I worked myself up to singing karaoke and almost simultaneously having a heart attack and stroke as my name was called.  My whole being was trying to run from the room but I walked right up and sang Jeremy by Pearl Jam.  I think it went okay and I have never stopped fighting the flight impulse ever since.

I would say this is the best way.  Everyone is drunk, most are awful singers, and quite a few are both.  You are SUPPOSED TO SUCK at karaoke so just do it!