Uh, so how do animals other than humans reproduce? They don't have human souls. And what about changelings?
Gross out Factor: Tapeworms carry both male and female genitalia. They don't need a partner.
All that we presently have on the Skinwalker is this, as told from Bob's (slightly anecdotal) point of view in Turn Coat, page 212-213, hardback edition: "You're using the English word, which doesn't really describe them very precisely. Most skinwalkers are just people- powerful, dangerous, and often psychotic people, but people. They're successors to the traditions and skills taught to avaricious mortals by the originals. The naagloshii." "Originals like Shagnasty", I said. "He's the real deal, all right," Bob replied, his quiet voice growing serious. "According to some stories of the Navajo, the naagloshii were originally messengers for the Holy People, when they were first teaching humans the Blessing Way." "Messengers?" I said. "Like angels?"
"Or like those guys on bikes in New York, maybe?" Bob said. "Not all couriers are created identical, Mr. Lowest-Common denominator. Anyway, the original messengers, the naagloshii, were supposed to go with the Holy People when they departed the mortal world. But some of them didn't. They stayed here, and their selfishness corrupted the power the Holy People gave them. Voila, Shagnasty."
And as for the procreation issue, here's what Bob had to say about it on page 212: "It's a semidivine immortal, Harry. It doesn't procreate. It has no need to recombine DNA. That means that gender doesn't apply. That's something only you meat sacks worry about."
Based on that statement, it seems as though there are quite a few things running around that don't have procreation requirements, but may also have souls regardless of that factor. Shaggy was created as a messenger, initially- which places him way outside of any category we've come across in the past, because he's not based on the typical definition of life.