Why is Corki bald?

Where else do you think the hair for that magnificent mustache came from?

retcon

Not all yordles are furry. Poppy and Tristana have no visible fur, compared to Teemo and Ziggs. From what I gather, Tristana started out as a "Megling" until Riot decided to retcon them into yordles. Additionally, Corki was originally designed as a human named "Cork". (Concept art here if you're interested: http://leagueoflegends.wikia.com/wiki/Corki/Background )

But that's not really important because we don't know for sure that Corki's bald because we've never seen him hatless, and maybe he shaves his face for that mustache.

Racist stereotypes? C'mon... We're better than this.