soak everything in a bleach-water mixture, then hang it out on a line to dry
But srsly, from my own non-professional experience, using compressed air should be okay to use while running, as long as you don't disrupt the airflow of the fans for too long. For the screen, the best thing to do is to use a cloth, like microfiber, that son't leave fibers, or cause too much static, and a cleaning solution without alcohol, like the blue gel stuff, so you don't damage the lining of the lcd.
Cleaning the keys is alot harder, try a vacuum with a brush atachment, or if you feel daring, or if it is possible, pop those babys off and do it up right! but make sure you put them back in the correct position lol