Funnily, those screws also sort of fit into the grid on the back of my computer case, so I mounted the old cooler externally, and it helps draw the hot air out. No reason to throw away a good PWM-controlled fan if you have a free connector on the motherboard, after all.

If you're doing it for the first time, try a few times without the thermal paste so you get the feeling of it. Then the pins will also go down easier when you do it for real.