I believe there is more of a Halachic incentive to obligate women to wear sunglasses than to forbid it. The Rabbeinu Yonah in Brachos has Shittah that (as far as I’m aware) no one holds by that states that anything that a woman is praised for in Shir Hashirim is an Ervah. So eyes should be an Ervah and any woman who wants to be Choshesh for that would have to wear sunglasses or tinted glasses to prevent her eyes from being seen. (And yes, the bigger the lenses the less likely it is that someone will see her eyes.)
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