Most of the CPU heat comes from the middle 2/3 of the CPU. The direction of the cooler 90 degrees or 180 degrees will make no difference if you applied the paste correctly (it should be thin enough to almost see through to the metal, almost fog like). What's there you can just smooth it out with a small plastic flat edge and reattach the heat sink.
However, if you want to start over from scratch without using an alcohol-based solution, you can use a non-lint producing microfiber towel or coffee filter. In a pinch a paper towel will work too, but be sure to look closely for any lint from it left behind. I would also recommend removing the CPU from the motherboard when doing this.