Shamone comes from the Michael Jackson song " Bad " released in 1987. It is a distinctive deliberate mispronunciation of "come on" used frequently by Jackson, occasionally spelt "cha'mone", "jamone" or more commonly "shamone".
It's a colloquialization of "Shamu", as in "whale". What he's saying in these lyrics (not intended to necessarily be interpreted as applicable to himself) can be paraphrased as "I look so fine to myself in this mirror, but when I go out only the Shamus come round." Remember everyone, this was 40 years ago; that's how males were indoctrinated to think. I'm sure we've all grown since.