Need to hang mirror, AC detected from stud finder
If the mounting hardware would hit a cable, you need only move the mirror a few inches to avoid it.

Cut a small hole in the drywall / plaster and look in the wall.  See where the cables go and hang the mirror in a way that doesn't hurt them.  Cut the hole in a place that the mirror will cover, and you don't need to worry about doing a good repair job on it.