Is there a difference in attack speed among one handed weapons?
Solution 1:
No, there is no difference.
I just crafted a Level One Dagger, Sword, Mace, and Axe on my Nightblade. The only thing on him that affects attack speed, is Rank 2 of the Agility passive, giving him +10% attack speed at all times. Between runs, I didn't change anything besides my weapons.
Running one of the weapons with a shield, I consistently timed ten heavy attacks as taking roughly 19.5 seconds. Running any combination of two of the weapons consistently took 18.5 seconds or so. Weapon type had no impact at all.