TT, I think pshat in Tosfos is that at the time the gemara made the diyuk zkancha vlo zkan ishtcha, the gemara thought that any growth on a woman is just considered a few abnormal hairs, but does not have a din of a beard, therefore hashchasa is permitted. (ALthough the pasuk does use the word zakan in the diyuk, it means your hair is considered a zakan, but a woman’s hair is not considered a zakan.) But once the gemara brings the braisa that zkan isha vhasaris sheheulu saar harei hein kzakan lchol divreihem, the diyuk is insufficient to tell me that hashchasa is permitted now. The diyuk only told us that a woman’s hair does not have a din of a beard and that was the ptur in the hava amina. But now that the braisa says it does have a din of a beard, what is the proof that hashchasa is permitted on a real beard? So we need the Gezairah Shava of peah peah mibnei aharon that even though a woman’s facial hair is considered a beard, hashchasa is still permitted.
Kach nireh l’aniyus dati.