Well, it does become complicated once you move outside the US. Peter Pan went into the public domain in the UK in 2007, 70 years after Barrie's death. Pygmalion will remain under copyright in the UK until 2020 (70 years after Shaw's death) but is in the public domain here. (The governing factor in the UK is the date of the author's death, not the date of publication. There may be other factors that I'm not aware of. My research was of a CYA nature and so not exhaustive, and thanking merciful God, I am not a lawyer.) One quick way to check copyright status of major works is to see if the US Project Gutenberg site carries the work.
The legal status of borrowing characters is a gnarly one (what you're doing is in a sense fanfic) but if your publisher is in the US it shouldn't be an issue any more than publishing a new edition of the play itself. And if the character in question appears in earlier tellings of the original myth, you can worry even less. I haven't read Pygmalion in 38 years or so (and you're much more up on myth than I am) but unless the character is one that Shaw made up out of whole cloth, I don't think there's an issue at all, even in the UK.
no subject
The legal status of borrowing characters is a gnarly one (what you're doing is in a sense fanfic) but if your publisher is in the US it shouldn't be an issue any more than publishing a new edition of the play itself. And if the character in question appears in earlier tellings of the original myth, you can worry even less. I haven't read Pygmalion in 38 years or so (and you're much more up on myth than I am) but unless the character is one that Shaw made up out of whole cloth, I don't think there's an issue at all, even in the UK.