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!