Just a word of caution, reinstalling the heatsink several times before plonking it down again could trap air bubbles between the CPU and the heatsink. This will affect performance of the thermal paste since air is an insulator but of course since you're not overclocking this method may well work for you.
Btw Pob I have never heard of anyone using their CPU cooler as the 'spreading device'
I have always used a piece of cling film wrapped around my finger to do the job. Just apply as small an amount as you can muster (ie rice sized) and wrap a small piece of cling film around your index finger (pinch it at the back with your other hand to keep it taught). Now rub the paste horizontally to either side with your finger so you have a line of paste running from left to right, then work your way vertically smoothing it up and down till the heatspreader is covered in a thin layer. If you make a mistake don't try to rub over it because that won't work, just remove all the paste and start again. Hope that helps