I'm planning on fixing the heat shield over my muffler soon. The rivits that held it up are completely gone/rusted through. Since the rivits are where the holes would be, I need to drill new holes into the frame. Are there any wires or lines that I would need to be wary of before I go crazy with the Dremel?

No wires run through the frame. The only things to watch for are brake lines and fuel lines, clearly visible on the inside of the frame.