Why did Mace Windu threaten Jango Fett on Geonosis?

Inspired by this answer to the question Why did Jango Fett jump into the arena to engage Master Windu?

At the beginning of the Battle of Geonosis, Mace Windu had managed to sneak up on the Separatist leaders. He revealed his presence by activating his lightsaber and holding it to Jango Fett's throat. But why does he do this? I understand that it wouldn't have been the Jedi way for him to just start slicing them up from behind, but shouldn't Count Dooku have been his main target? What's more, Fett was a mercenary who was working for Dooku and the Separatists. Did Windu think that Dooku would care about his life?

Apparently, Mace Windu later regretted this decision. From Shatterpoint:

In my dreams, the purple flare of my blade sizzles the gray hairs of Dooku's beard, and in the critical semisecond it takes Jango Fett to aim and fire, I twitch that blade and take Dooku with me into death.

So why did he target Jango Fett instead of Count Dooku in the first place?