I think that's a great start to a trimmed down version of the Episode III opening, but I don't think the movie works without seeing Anakin take out Dooku. For one thing, it's the start of his fall to the Dark Side and there are already precious few good scenes dealing with that in the movie. Also, it'd be terribly distracting and nonsensical if the only thing we hear about Dooku in Episode III is some throw-away "oh yeah he died" line from Sidious when he's talking to Grevious.