Jumpman is right. The Hero's Shade isn't a stalfos, but a ghost. From what I remember, he's called the Hero's Spirit in the official Japanese translation (or was it the other way around..?)
Anyways, he's most likely a ghost, seeing that only his face is skeletal, while the rest of his body has an ethereal presence about it.
Also, if he were to become lost after his adventure in Termina, then he would become a skull kid - not a stalfos. Adults turn into stalfos, children turn into skull kids (or stalkids, which is what they're call in the original Japanese translation.) Kokiri don't turn into anything because they have their guardian fairies to protect them at all times. This is also confirmed through Fado's dialogue, as well as the Lost Woods gossip stone - in both the original and 3DS versions.
Also, it's kind of hard to accept that a twelve year-old child can transform into a 7-foot, adult, undead spirit in full-blown royal armor; even by Zelda standards.
EDIT: PS - There's a growing amount of evidence that The Hero's Shade may actually be SS