I absolutely agree with Mrrzy's point, also demonstrated by Yvonne, that the bartender must ask the question. I think it works best if it's indicated that the bartender looks at him as if not quite recognizing what he is, then asks with an inflection indicating a dawning awareness, "Say, aren't you a (piece of) string?"

I disagree about using the word "no". I think it sounds more natural for the string to say "No, I'm a frayed not/afraid not."

It also helps impart maximum impact to NOT use the words "frayed" or "knot" while setting it up, but of course you have to describe the fraying and knotting in some manner to maintain continuity and make sure everyone "gets it". Mrrzy's example above does that well.