This is not entirely true. When adding attack power to normalized, weapon-based attacks, the type of weapon used determines the multiplier applied to the attack power contribution to weapon damage. One-handed swords, fists, maces, and axes receive a 2.4 multiplier, while daggers only receive a 1.7 multiplier. So even though a dagger might have a higher average damage than an axe/fist/mace, the axe/fist/mace will most certainly win out due to the extra 41% of AP scaling -- unless the dagger is of significantly higher item level than the axe/fist/mace. This is especially true of abilities which give a percentage damage bonus as part of the ability, such as Lava Lash.
Lava Lash receives the following damage bonuses:
+ 300% - baseline
+ 40% - if using Flametongue Weapon on the off-hand
+ 20-100% - Depending on stacks of Searing Flame
There's a potential for +440% weapon damage done by Lava Lash. Since the AP contribution is added to the weapon's damage to determine the overall weapon damage before applying ability bonuses, this means that an axe/fist/mace receives an extra 180.4% AP contribution which is very hard to overcome with a dagger.
Stormstrike works similarly, with a +450% boost to weapon damage. Thus, for Enhancement Shaman, daggers aren't even worth considering unless you're upgrading from something like questing greens to a ToT dagger. Even then it might not be worth it, would have to do some more math on that.
See
Weapon Normalization for more details.