Why not agility instead?
If we were real warriors you would not have to ask, you would know from experience.
Here is your homework:
Step 1: Get a very light weapon. A knife, for example. Swing it with one hand, then swing it with two hands. One-handed mode will be faster, for many reasons. The most important are:
1) It is easier to coordinate one hand than to coordinate two hands
2) Not both hands are equally skilled. One can do better than the other. Using two hands means that your maximum speed (without suffering from coordination problems, see above) will be dominated by your slower hand.
Step 2: Continue the experiment by taking heavier weapons.
Sooner or later, probably sooner, you will get to the point when you find that using two hands makes it easier to handle your weapon. With two hands, the weapon will be faster.
Reason is that the weapon you are using is too heavy for your strength.
Step 3: Get some muscles. Then get back to the weapon. You will be able to swing it faster. When you have increased your strength high enough, you will - again - be able to use it with one hand faster than with two hands. (Of course this only works till the final level of fitness a human can reach - so dont tell me 'Damn, I am training in the gym 6 hours a day but I am not able to swing my 30-pounds-hammer with one hand faster than with two hands'.
I am talking about one handed weapons.
In-game, it could work similiar to the influence of shield skill on its speed (and damage).
Example:
y = factor (in this example y = 1, counter all 3 attribute points like its for all the skills)
Weapon X's requirement is 12 and its base speed 98.
Char A has 9 strength. He is so weak, he cant even use that weapon.
Char B has 12 strength. He can use the weapon, but he is so weak, so he barely can handle the weapon properly. Speed penalty for him. Speed for him (base speed 98 - y (in this example 1, see above)) 97
Char C has 15 strength. He is strong enough to use the weapon okay. No speed penalty for him, no bonus, weapon speed = base speed = 98
Char D has 24 strength. He is strong enough to handle this weapon without any problems, more than that, in his strong arm, the weapon feels as light as a pencil.
Weapon speed for him: base speed + 3y = 101
