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!