Whenever I enable sweeping edge, every kind of sword has sweeping edge no matter if the enchantment "Sweeping Edge" is on it or not, even if the sword has NO enchantments, it still has the Sweeping Edge affect

Do you mean the Sword Sweep attack? All swords have that, the Sweeping Edge enchantment just makes it deal more damage.

So there is no way to have it where only swords enchanted with Sweeping Edge will have the sword sweep attack?

There's probably a way to have that, but I don't believe it's the concern of this plugin to implement such a feature.