Wario was made to be an exaggeration of mario so to further exaggerate mario puffy moustache wario gets a zig zag one.
Delving into head canon territory, he never combs and considering transforming and how many times he gets burned or shocked.
I reckon old lightning-tache always had ingenius facial hair - not least because it forms a dastardly "W" shape on both sides of his face. It also reflects just how crooked he is.
As a former villain, he had a bad habit of pulling his mustache when something went his way, or when he was waiting for Waluigi to get out of the shower. What? the man needed something to do while he waited.