Sneezing While Not Sick

My girlfriend and I disagree on whether you should always wash your hands after you sneeze. She seems to think it is only to prevent colds and other illnesses and therefore if she is not currently sick, there is no harm continuing cooking or whatever else she is doing.

Is it possible to have a "harmless" sneeze? (if possible, refer to medical textbooks or studies).
I get queasy imagining someone sneezing into their hand then making me a pizza or shaking my hand.