Except that a dragonborn doesn't have the ability to turn into a dragon. Martin Septim was the only one to do anything similar, and he only turned into a dragonfire statue because of Akatosh and Mehrunes Dagon. Also, Martin died from it, so it's not exactly high on my wishlist.
martin used the power of the amulet and his blood to summon an avatar of akatosh, he didn't transform into a dragon but summoned one.
also martin was never trained in the ways of the voice so dragon shouts were a little bit out of his reach at the time.
dragons are rumored in the lore that they have the power to shapeshift at will to disguise themselves. and we now know that most of a dragon's abilities stem from the use of their language.
going by that logic it's perfectly possible for a shapeshifting shout to exist.