First, I do not recommend using rubbing alcohol on anything related to electronics because this type of alcohol leaves a residue behind that does not evaporate nor is water soluble. I personally have used Isopropyl alcohol on motherboards and other electronics with satisfactory results.
Isopropyl alcohol is sold in drug stores and grocery stores with a 70% by volume ratio, it does evaporate and leaves no residue behind.
When I clean out the inside of a computer case, I use the following list of items: A wrist strap worn to prevent static discharge damage, can of compressed air and a toothbrush.
The toothbrush bristles can be trimmed down so the brush fits between the blades of the cooling fans. This removes most of the stubborn, stuck on dust you spoke of quite easily.
You might actually find that using alcohol at all is more of a extra added burden, because you have to waste some time waiting for it to evaporate. Cleaning a dry dust is easier than cleaning a wet or moist one.
The can of compressed air finishes the job of blowing the loose dust out of the case entirely.
Any time you do any work on the inside of your computer, please be sure to practice the correct procedures that prevent damage to your computer caused by static electricity. It does and can happen.