The whole plot is just so convoluted, I would just as much buy that Palpatine had orchestrated every little event in the movie as buy that the Jedi starting the war was only the result of Obi-wan’s investigation.
So why would Dooku erase a whole star system from the archives? He is obviously aware that you can’t actually do that since Hyperspace navigation requires precise calculations. We can’t have ships flying into missing planets or being flung wildly off course, so gravitational effects must remain. If the reason was that he didn’t want the Jedi to know about the clone army, I’d argue that a more effective way of doing that is not drawing attention to yourself by deleting a planet from the Jedi archives, a planet that people know about and that is home to a highly technologically sophisticated and wealthy species. If Dexter had just said that the dart had come from Kamino, it’s possible that Obi-wan would have simply assumed that was where the bounty hunter bought his weapons, not where disgruntled Spice Miners on the Moon of Naboo had hired their bounty hunter. That was after all the leading theory of the Jedi as to the source of the assassination attempts, so the Jedi could have demanded that Obi-wan go investigate that moon instead of Kamino. It is only after they discover the star’s deletion that Yoda gets suspicious and demands that Obi-wan take the trip.
If I were making bets, I’d say that there was a good chance that Dooku deleted the star system on orders from Palpatine, or even that Palpatine deleted the system in order to draw attention to the absence.
Another thing, why does Jango lead Obi-wan right to Geonosis? Unlike Kamino, this system hasn’t been suspiciously deleted from the archives, so if it was Dooku who wanted to delete planets to keep things secret, he forgot this big important one where they’re literally planning to build the Death Star. Perhaps its role in the war happened after Dooku could no longer access the archives. In any case, why did Jango go there? He knows he was just tracked down by a Jedi, does he think that he’ll be safe on Geonosis? Why not just go anywhere else in the galaxy that’s not the secret base of your employer? It’s the same problem that happened in ANH, where the Falcon could have gone anywhere else and gotten rid of the tracking device.
My guess is that Dooku fully intends for the Jedi to find Kamino and Geonosis, and although he is working for Palpatine, he secretly plots the overthrow of Palpatine and the defeat of the Republic. He’s an idealist after all, and though he goes along with Palpatine’s plan, he believes that he only does it to get close enough to Palpatine to put the proverbial knife in his back. So in Episode 3, perhaps he was the one who, alone, led the attack on Coruscant to capture and perhaps kill the Chancellor.
Perhaps the Clone Wars explain the character of Dooku, but I DON’T WATCH IT.