When was the last time you heard someone use that in conversation or, really, anywhere? Please don't cite writing that's 60 years old.
I've never heard anyone use the term fair to describe a woman in any context.
I have. I agree with Leah, that it's a bit tone-deaf, but I still have relatives who use it as a rather heavy-handed attempt at gallantry. From them it's always sort of sweet - but not something I'd encourage in general chat...