I might addd that a 3 or 4 pin fan is a bit overkill. You just need something that spins. You don't need any comms in the fan for this project, so a 2 pin is fine and you'll pick that up for next to nothing on eBay. Might not last as long :)

As far as the last point of step 2 goes, I would add to the parts list a can of compressed air to get rid of all the dust on the screen frame and the interior body once the lcd is off). When the magnets clip back in dust will shower down onto the lcd and glass if you do not clean the frame well. It will not matter how much you clean the LCD and inside of the glass panel.