Well, it states that it is not cummulative with Haste. I guess that is open to interpretation, but basically the rest of the description talks about the extra partial action of Haste and the extra partial attack by the weapon. That seems to be the focus, so that is probably what is meant as not cummulative.
There are no rules there for two weapons of speed not being useable at the same time. Each gives an extra attack with that weapon, just like two flaming weapons give their flame power to an attack from the individual weapon.
It does not state that they are not cummulative with each other, it states that they are not cummulative with Haste.
This is how I would rule as well.
Each weapon gives an extra attack for that weapon. Nothing to indicate that they are mutually exclusive.
Each weapon should only get the extra attack when Hasted if the extra partial action for Haste is not taken.
So, with two weapons of speed, you get:
1) All aspects of Haste, nothing from the weapons OR
2) All aspects of Haste except the extra partial action and a partial attack from each weapon.
Your choice.
If not hasted, you get an extra partial attack from each weapon each round.
