At the risk of sounding blasphamous, I would say that He would be genetically a woman if His was the flesh of Theotokos. And, technically speaking, there was no conjunction of genetic material; He would have XX make-up, a Barr body, and no Y chromosome. I am not questioning if that is possible -- I am saying that for Him to be "fully man" as we are in every sense but the pre-Fall state does not agree with our understanding of humanity biologically, as it is implied when we say "in every way human" like us.
There is, of course, no direct answer to your question, either in Scripture or even in our voluminous Tradition!
All that I would say is that if Adam and Eve were created de novo and were fully human (and fully male and female, respectively), then it doesn't seem that unlikely to me that God could create an extra set of chromosomes (including that elusive Y chromosome!) from the flesh of the virgin. The raw material of amino acids and what-not were all there.
If God could make an entire woman from Adam's rib, he can certainly do that! The Scripture doesn't say that Mary would spontaneously form a child, it says that she would be overshadowed by the power of the Holy Ghost, causing her conception -- that's pretty powerful stuff. There *was* a Father involved, even if we completely reject the Mormon idea that carnal relations took place.