You can use a piece of tape. Cut it to the angle needed to place it in the corner, then try to apply it as straight on as possible. Pull it off after a few seconds and much of the dust should come with it. Repeat as needed.
well at first glance i was really impressed with your idea, but when i read wolf's counter-idea it reminds me that it really can leave sticky marks on the screen, have you tried this trick of tape yet, did it leave such marks?