On swearing: As I recall, there's a commandment against taking the Lord's name in vain, whatever that originally meant (It may have meant perjury.), but I don't see anything in the Bible against saying "shit!" This comes under the heading of politeness. Saying "shit" may be impolite, but I don't see any reason Christians should be more polite than other people -- or that anyone should be more polite in the presence of Christians than at other times.

Still, politeness is a good thing, and I commend your effort to be polite in a public performance.

It wouldn't have been impolite for you to go the mike immediately (when you were introduced prematurely) and say, "I'll be ready in about 5 minutes [or whatever]." This would have given the MC the choice of how to fill the 5 minutes.

Or, you could have filled the 5 minutes yourself with some inconsequential chatter while you bandaged your finger, tuned your guitar, etc. But generally, only people who have had a LOT of experience in front of audiences can do this comfortably. And maybe even they aren't comfortable, but if they convincingly LOOK comfortable, they help the audience feel comfortable.

Even the best performers occasionally have to deal with mishaps: a broken string, a mike that won't work, forgotten words, a low-flying plane that drowns out the sound at an outdoor concert, etc. The next time you see this, pay close attention to how the performer handles it. The best, most experienced ones will INVOLVE the audience in the crisis by explaining exactly what happened (if it isn't obvious, like the airplane), thereby gaining their sympathy, and maybe getting them to laugh about it.