That is not really a deleted scene, and more of a discarded concept born from the process of the production trying to execute the Dooku/Yoda duel properly.
Even then, I believe the idea was that he uses a fallen lightsaber in a desperate attempt to block Yoda's counterattack and he's holding one of the stunt lightsabers from the arena fight so he's not dual wielding because he wants to.
It's good that the idea was never used because it does go against his character as it became more fleshed out.
While no longer canon, in Labyrinth of Evil, Dooku states, "What was to become of elegance and gallantry if a duelist couldn't make do with one blade?"
Both in Legends and current canon, Dooku was known as an accomplished duelist; one of the best in the Jedi Order.
He is identified as a practitioner of Form II Makashi lightsaber combat, which focuses primarily on single blade to blade combat with careful and precise strikes.
This is at odds with the method of Jar'Kai (dual wielding), which favors other forms like Ahsoka's Form V Djem So/Shien.
So it is correct to say that Dooku would not dual wield by choice.