The text plays on the phrase 'if it ain't broke, don't fix it,' suggesting that something should not be tampered with if it is functioning properly. However, 'let me have a shot at it' introduces a double meaning: one interpretation is to attempt to fix or meddle with something, and the other is a humorous suggestion that the speaker might break it if given the opportunity. This relies on the ambiguity of 'have a shot at it' for humorous effect.
If it ain ' t broke , let me have a shot at it .