Student or Learner
"But I warn you the beauty will only be skin deep," said the wizard.
"That's all right," replied the happy glass-blower; "when I lose my skin I shan't care to remain beautiful."
Thank you Raymott
The expression 'care to do something' is quite old-fashioned and means something like mean/want/choose to do it:
'What's your name?'
'I don't care to answer that'
'If you'd care to look out of the left-hand windows, you will see <whatever>'
Thank you, BobK
In a similar vein, humorist Jean Kerr once said "I'm tired of all this nonsense about beauty being skin deep. That's deep enough. What do you want, an adorable pancreas?"
The speaker in your quote has the same attitude - if beauty is only skin deep, it's OK with her to simply have beautiful skin, or, to be beautful in appearance only. She doesn't care about her "inside" being beautiful.