The stud finder sucks, those give false positives for electrical all the time. You're probably fine if the wall isn't riddled with outlets, switches, or has a breaker panel.
If you're really concerned, drill through only until you're past the drywall. It's only about a half to five eighths of an inch thick. Wrap a little piece of tape around your drill bit as a depth gauge. Alternatively, there are drywall anchors that look like fat plastic white screws that don't require a pilot hole. You can get those and avoid drilling entirely.