We do not have an exact pronoun that you are looking for.
is the most formal, but it is **completely** gender-free.
**** is **mostly** feminine, if not completely, and it is a tiny bit less formal than for using the . Perhaps it is a good candidate, all things considered. At least, I could not think of a better pronoun for your purpose.
In Japanese fiction, **** (more often written **** ) is often used as part of "role language" for a sophisticated dame. Fake or real sophistication, it does not matter.
(I said "mostly feminine" above because despite the wide-spread rumor among Japanese-learners, quite a few older gentlemen [especially around Tokyo] do use **** and **** . They used to use **** as well.)