I'm perfectly fine with a teenage Spider-Man, I'd even say that's my preferred route to take. Spider-Man is a huge influential character in the Marvel universe for me, and whilst adult Peter is pretty awesome, him being one of the youngest heroes in a world of adults always made him stand out more for me, and the threats he faces seemed much more intense to me when you gathered the fact that it was a teenager fighting to protect a city of millions, often on his own. Even without the origin story (which you don't need), it would be much better to have the character grow throughout the MCU, for both storytelling and character-development purposes.
Dylan O'Brien all the way for Peter Parker btw. I like Logan Lernman as an actor, but he's outgrown it a bit, and based on O'Brien's work from Teen Wolf and The Maze Runner I can easily see him nailing both the Peter Parker and Spider-Man aspects of the role.