You can definitely replace the switch. My reverse lights went out about 8 months ago; the switch caused the problem. I had my car fixed under warranty, but I don't think the switch is that expensive.. probably under $20.
Like I said - Take the plug off the switch. Put a pair of pliers between the contacts in the plug (i.e. connect the two wires in the plug with a metal object - not the ones on the switch). If the reverse lights come on when you short the wires in the plug to each other, it's the switch. If they don't, it's some other problem.