Well, if you screw up the keyboard you could always get a slim USB or PS2 one (I assume the laptop has a PS2 port), and the cables on those are easy to mess with.
You are correct on the monitor cables. The bundle of little wires on the left are the signal wires. The small circuit board on the right is the power inverter for the backlight, so the two wires coming out of it are carrying a pretty high voltage load. With that in mind, personally I would extend the wires leading to the inverter instead of the wires from the inverter to the backlight. If you do decide to extend the wires from the inverter to the backlight, I would recommend some high-temp solder and high-voltage wires. You can pick both up fairly cheap, you just have to know what you're looking for. Other than that, yes, normal twisted copper wire will work fine for everything. I would not recommend using solid-core wire or aluminum wire though.