I think I understand what striker410 meant; that changing the cooler is more effective.
Six degrees seems like a large drop on an i3 with the stock cooler?
But it's all a bit moot because the OP already has the paste...@bubblehearthlol:
You could take the view that now you've bought it you may as well use it. Alternatively you could take the view that the benefits of a 6 degree reduction don't outweigh the pain of having to remove old paste, apply new stuff, then reseat the cooler.
I use ArctiClean
to clean up old paste and prepare the surface.