First: Thanks for the mention.
So far, the best alternative seems to be referring to them by their particular style, like men do: briefs, boxers, boxer-briefs, long-johns. We could call them thongs, boy-shorts, G-strings. Et cetera.
Actress Christina Hendricks, in 2011, told Esquirethat “Panties is wonderful word. … It’s girly. It’s naughty. Say it more.” Personally, though, I don’t know many women who would agree with her.
If you “women” do not measure up to this lovely creature, it is called ENVY. That’s why most “women” “would” NOT “agree with her”