sure, ignore it, be a d*ck, it really shows of the good sides of your character...
Do you have to shake the persons hand before and after a game?
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You can if you want to but that's very unsportsmanlike and all it would do is shorten your life time but anger.
How would it shorten his lifetime? All it could possibly do is prevent him from catching a viral disease.
Most people at live tournaments won't be obnoxious about winning; many will even offer to analyze the game, play casual chess, or otherwise befriend you. Refusing to shake the hand of someone like that is sort of like kicking a puppy or not giving your bus seat to a disabled person.
Or can you ignore/refuse it? Sometimes when I lose I get very angry inside. I know its not the other persons fault because its blunders on my end or they played well. But sometimes when people offer to shake hands, I feel like destroying it especially when they talk crap after.