I assume that like with Keros' TF, Lumia won't turn us into a full fledged valkyrie so it could make sense for a faux-valkyrie to be male. Besides, the champion strikes me as the kind of person who doesn't give a fuck about rules and convention so the the idea of them being the sole male valkyrie would be totally in character.
Well, I think there's a difference between the Kitsune and the Valkyrie, in that the Kitsune can get born, but the Valkyrie are
only created through godly intervention. Similar to the Gothmanders, they only exist from the gods creating them. Also with the Kitsune tf we essentially turn into one, given the extended lifespan (only godly tfs can extend the Champ's lifespan), the only thing I know that's different is that we have a faux soul to trick demons rather than having no soul, and even so, I think we may still be connected to the communal soul (though I'm not certain), we just have a little extra.
So, you can't really say it's a faux-Valkyrie, when there are no natural Valkyries. The Valkyrie form is based on Boreal Elves, and we aren't one until we get transformed into a Valkyrie. Even if we take the Boreal Elf tf item, item tfs don't change your core, and your age does not extend with it. However, it will extend with the Valkyrie tf, to have a Boreal Elf lifespan (so you can now spend Etheryn's life with her, rather than dying halfway through from old age). So, I'd say calling a divine tf a "faux" form is off, as they're the only transformations that can
fully transform you into that species, or at least enough to have a matching lifespan.