Leopard Lizard nailed it.   The other suggestions were all great for helping to IMPROVE your singing, but to get up and just do it you need the right attitude- and a sense of humor is a great start!  Remember, Karaoke is all about having FUN.
   You might start at home with your wife.  Worried about looking like a fool?  Guess what?  Your wife already knows all about you, and loves you anyway... 

   So no worries there.
   You might try starting with duets. This is how I get less confident people started at my shows.   The number one starter duet that comes to mind would be you and your wife singing "I Got You Babe" by Sonny & Cher.  Almost impossible to to hurt badly from your point of view- remember Sonny's vocal skills?
   Get up and give it a try! You'll have fun, and want to do it again.   See how you do, THEN go the improvement route.
   BTW: A little "liquid courage" may be helpful as well- at least to begin with. Just don't overdo....  GOOD LUCK!