Interesting theory, but there is nothing in any of the games that can support it.
It was always questioned, at least by myself if Gerudo were an all female tribe, exactly how did they have kids. Breath of the Wild explained this that Gerudo seek outside relationships with other cultures (I assume Hylians for the most part). If Zelda worked like real science though, the Gerudo would be doomed to extinction because every single child they'd ever have will be half Hylian, thus their half Hylian child would end up having a child with another Hylian, making them only quarter Gerudo, and so on and so on.
So Gerudo I do believe is all female, but they're able to sleep with Hylian men from outside the city walls and have full Gerudo female children, sharing very few or no Hylian traits at all. Perhaps that one lone Gerudo male probably is born out of a fluke, in which he does inherit enough of his father's genetics to become male, and he just so happened to become King due to their customs.
It could also be possible that Gerudo has never had male children other than Ganondorf, since he wasn't born by any normal means due to a spoiler in Skyward Sword. If it is possible that he is the only male Gerudo ever born, they probably considered that exceptional and thus felt no other way to approach the situation but make him King. This is likely possible, since there is no existence what so ever of another male being ever born in the Gerudo tribe. It's only implied, but without enough detail to ever know the full situation.
If I got anything wrong here and anybody like to point that out, please share. I might have missed a fact or two. Or probably many, who knows.
(Note: I also like to add that it also never implies how people are born into this world. It is assumed that it works the same for the people of Hyrule as it does for us. I just know Nintendo has no interest in teaching the birds and the bees in their games).