OoT Link (who I firmly believe is the Hero's Shade) probably uses a wolf as his spirit form to put TP Link at ease, and to make him relatable to. It was an intentional link (haha, no pun intended) on Nintendo's part to signify that TP Link and OoT Link are related. They both take the form of a wolf and are destined to save Hyrule from Ganon. And he has to become an undead warrior in the ethereal spirit world. How else would he teach TP Link his sword techniques? It's just a matter of choice on his part whether or not to take the form necessary at the time.
The spirit world the techniques are taught in is most likely where his spirit remains because he cannot be at rest since Ganondorf returns to Hyrule again anyway. After OoT Zelda is warned of Ganondorf, he is executed (even though it's a failed attempt) and sent to the Twilight Realm. Link's spirit was made to fight evil, so he can't be at rest until the evil is put down permanently. Ganondorf was not dead, just in an alternate dimension.
I feel like there is a gap in between MM and TP that should be filled with another game, or at the very least a better explanation. Maybe OoT Link isn't at rest bc he never found Navi! There are a million plausible explanations that Nintendo desperately needs to clear up.
(That made sense in my head, so I'm sorry if it got super confusing!)
.
