I think this topic has much to do with Augustine's dogma of "Sinful Flesh" and "Sinful Nature". I think we should define what is sin first.
Even today, Jews reject Catholic understanding of "sinful nature" and declare it alien to the Old Testament.
The Fall of Adam, didn't bring a sinful flesh, but more inclination to sin, because we have to work for our food. Adam was given wife from God, as well as free food. After the fall, you have to work for both, which arises a higher possibility for sin. (And also, we lost direct contact with God, so lack of faith is also an issue)
Thus: Hunger, Thirst, Sex - these things aren't sinful by nature and they can't be. But if you are hungry, sexually deprived, thirsty, you have higher inclination to do something sinful - rape, kill, steal or purchase a whore.
That's why even today, there are lot of atheists who are excellent in terms of morality except one thing - they don't consider sex out of marriage a sin. (And that's why Pelagius said that "Christian can and should become sinless.")
So regarding Christ, I don't understand why there is even slight idea that He sometimes wanted(or theoretically could have) to murder, rape or steal.
But to say that he was hungry when he was fasting, or he may have liked a girl/woman visually - this is not a sinful nature or even a sin. And could Christ have emission of semen as presented in Old Testament? What we call "wet dreams". If he didn't, he didn't have a human nature. (The Natural - emission of semen, or the menstruation - wasn't considered sin in old testament, while Augustine and some did)
Now I don't find it necessary to touch the idea of 1 or 2 natures, I think it's evident even without that.