The difference between arrogance and cockiness imo, stems from the fact that an arrogant person, ACTUALLY believes they are hot shit, and thus blinded to their flaws, or putting up a farce to shield their insecurities. A cocky person, doesn't take his shit seriously, and is mostly just playing around and being sarcastic, thus demonstrating true confidence and security; something women find much more attractive.
I totally agree with you, but I think the difference is very thin
Also, being cocky is no-where near as powerful as being mysterious.
What about being both?