No.

It would be his own DNA that gave him the attribute of being able to change into a canine. He would not be a human being, he would be a different species, supposedly descended not from when we split the primates up, but it would have to be way, way back, potentially as far back as Boreoeutheria splits.

Unless you wanted to add in some fantasy mad-scientist thing, where his DNA was somehow created artificially: in which case, this answer still stands: he has his own, unique DNA.