The term 'wingman' is a type of social colloquial phrase used amongst friends. If you ask someone to be your wingman you are effectively asking them to assist you in flirting with someone you're interested in. So for example if you were my wingman your role can range from, talking to the guy's friend so that I can talk to the guy I'm interested in alone, making positive comments/compliments about me so that I seem more attractive to the person who's attention I'm trying to get. But basically, the wingman's role is to aid the 'pilot' (that's the person who's trying to pick up a partner) in getting the attention of the male or female. If a women is aiding someone, she can be referred to as a wingwoman :)
So in the example you gave, Howard has devised a method he thinks will help him pick up girls better and wants someone to assist but Leonard disagrees, stating that if he uses those lines, rather than needing a wingman he'll need medical attention. It's implied that one of the girls will hit him (not surprising if you consider what his negative compliment entails) hehe.
But you got the jist of the conversation so well done :) I love Big Bang Theory too!
If there's anything I can clarify for you please feel free to ask me :)