1) I advanced the main quest to the point where I was looking for an Elder Scroll. Used a Shout to gain admittance to the College (I used Make Ethereal, but presumably any shout other than Whirlwind Sprint would work, and that one might even do it too)
2) Used Spell Breaker in place of a Ward spell in the quest where you are asked to demonstrate a Ward spell.
3) Used Fire Breath in place of a traditional spell in Saarthal, to break down the barrier. Presumably other Shouts might work, such as Unrelenting Force.
4) Tried to use Frost Breath in Mzulft. Failed to get the proper alignment, but I'm not 100% convinced that it's impossible.
5) Used Fire Breath and Frost Breath in Labyrinthian where a fire or frost spell was called for (the two doors with the spirits).
Combat was done with dual-weilding swords & wearing light armor - a fact which rather trivialized Labyrinthian which is set up to stymie spellcasters. So in conclusion, this can be done with only a few shouts. You will have Unrelenting Force and Fire Breath already, so you really only need to seek out Frost Breath and pick up Spell Breaker.

