Just to let you know, "ごきげんよう" literally means "I hope you are in a good mood". I'd say it is a polite way of saying "Have a nice day".

If a woman who was NOT born with a silver spoon in her mouth should say this way, it would sound a bit snobbish.

I guess you mean "ごきげんよう", though it is not a common greeting now in Japan.