Varies depending on your location and building codes there, but as a rule of thumb wires will go vertically or horizontally. Wires should not go diagonally through a wall. So don't drill in the column or row of a power point or switch.
Do remember walls have two sides, check the other side for switches and plugs and fuse boards.
Another option is to push through your gib/drywall with something non-conductive, in the spot where you want the fastener to be anyway. It doesn't take a lot of force to put a hole in drywall linings. An old insulated electricians screwdriver works well.
Once there's a small hole you can use a stiff wire through to sweep around and find anything by contact, although by this stage your hole is probably fine to use for the fastener.
If you want to spend money, a borescope can tell you what's inside the wall, but they need a hole of at least a centimetre to get the camera through, which is probably too big for your fastener.
Another option is to pop off the faceplate of any plug/switch fitting in the immediate area of where you're drilling, and use a torch/flashlight to see in what direction the fixed wiring goes. Naturally you want the mains supply to the circuit turned off to do this, and test socket before removing from wall.
If you have access into the roof space or under the floor then have an explore and see if there are power cables coming through the top/bottom plates of the wall and into the floor/roof cavities. Again, access is the deciding factor (along with your dimensions, flexibility, and overall interest :)