I noticed something very disturbing... And it can explain who it is.
It is Delphine, because she's a dragonborn ! or a cheater...
Let me explain, in that main quest where you need to find the Horn of Jurgen Windcaller, you know that Delphine stole it to meet the dragonborn ? but do you remember the little puzzle just after the room where the note is, yes the one with 3 pillars that light up and open the doors for like 1 second, you MUST have the "whirlwind sprint" shout to get over it. So Delphine must be another dragonborn, for those who dosn't know, it is possible to have several dragonborns at the same time, like Miraak.
Perhaps she does that to help the dragonborn getting stronger, wait... Miraak didn't want to fight before you get stronger... so... Delphine is Miraak ? (Ok i'm going too far )
Well I don't know why she would do that but Delphine is a dragonborn.
You don't need to be a dragonborn to learn shouts though. We are told that anyone can with enough hard work. The Dragonborns just have shortcuts in the learning process.
Ulfric knew at least one shout without being dragonborn or ever having seen a dragon before Helgen. The greybeards similarly aren't dragonborn.