Do not use thick compound. That is rule #1 and thus, you will not ever have to spread it (even if you did, it would prevent best contact between CPu and 'sink).
By thick I mean thicker than Arctic Silver/Alumina/etc, like old silicone grease. Further, do not use silicone grease on flipchips without a spreader, it will pump or dry out over time with today's high-heat-density cores.
Do not use heatsinks with an irregular surface unless (arguably) forced to do so - for example on proprietary video cards the base is sometimes bad but can only be lapped so much due to the design.
With the proper viscosity of compound, a very small amount should be placed in the center of the core. Not a blob that looks like an icre-cream cone, not spread out over a large area like frosting a cake, just like an itsy-bitsy pancake in the middle of the heat spreader or almost to the edge on cores without spreader. You are not trying to create a uniform thickness, the edges of this pancake should be see-through and only the middle opaque, but on the other hand you don't have to play around in it to try to achieve this ideal state, just an indication of how much to use and where it goes.
The (potential) mating area between an IHS and 'sink base is far too large to allow optimal interface by spreading compound over the entire spreader. That guarantees the compound is thicker than it otherwise would've been, and with that much surface area the heatsink retention force is not enough to squeeze out all of the excess.
Now about using a credit card or plastic baggie or any other special tools- don't be silly, there has never been any valid test proving that matters. If you have so much crud on your hands that you think "stuff" is going to come off in the compound, wash your hands! Oils from fingers- not significant unless it's been a long time since you've washed your hands. If you really like playing with special tools, they will work ok, providing application is still thin and in middle only, but they're not necessary.