Doo Rag, bandana types are quite different things and are thought (in a fashion sense) at least by those wearing them to be cool.

I am not sure if the knotted hankie is now thought to be so - or that it ever was.

I suspect that back in the days of the cloth cap (the heyday of the knotted hankie) - when on trips to the seaside - this would be left behind perhaps as a symbol that normal conventions were not applicable for this time. And perhaps quickly put back on for the return home and that the knotted hankie was a form of headgear and security to those who wearing some form of headgear was the norm.

Just as you would not wear a knotted hankie to work - wearing a cloth cap on the beach - would have been thought to be a similar fashion mistake