Just make sure they aren't the cheap ones, I have quite a variety of Q-tips and the more expensive ones don't leave lint whereas the cheaper ones that seem "fluffier" leave quite a bit of lint on stuff.
Eh, they're kinda fluffy but what q-tip isn't? I can just blow any fluff off when I'm finished right?
Also, could the friction from rubbing off the paste create static that could damage the CPU?
I've rubbed the processor with a Q-tip in a reasonable way and no damage was ever done. And I've cleaned numerous processor and none have been damaged by static. Just make sure you are grounded and have no static on yourself and your good to go.