Shake girls hand when introducing?

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So at my work there is this girl who ive been trying to work up the courage to talk to. And i think she knows it. When i walk by her, she makes eye contact with me on purpose. It might be the "say something already" eyes or maybe "stop talking me" eyes. most recently i walked by, didnt look at her, could tell she was looking at me tho so i turned my head and she gave eye contact for like 3 seconds. So im thinking i need to do it NOW. So heres my plan. walk up and say

"Hey, you know. Ive worked here for like a year, and i havent said hello. Im soandso."

do u think thats a good icebreaker? do you think i should shake her hand or not? should i ask her out sometime or save that for another day?