Take the computer out to the shop and blow it out there. Not sure if I'd use the shop compressor though. It might be too powerful.  Buy those cans with compressed air and blow it out good. Do not spin the fans as you might damage them if you over rev them. Let the computer warm up to room temperature before turning it back on. If you turn it on cold you might damage some components.

As for the dust in the house, unless you want to spend big bucks to climatise the room, I don't think there is much you can do other than to throw a cover over the box while you're making dust.