Can I skip the investigation in 'Blood on the Ice' if I know who the killer is?

This quest annoys me.

Before the court wizard is even falsely accused of the murders, I can pickpocket Calixto's key and find direct evidence in his chest that he is the one responsible for the murders.

In spite of this, I can't seem to present that as evidence from the start, causing the

court wizard to be falsely imprisoned when I already have the evidence to prove otherwise.

Am I missing some way to first show the evidence that

it's Calixto from the get-go?

Once you have the strange amulet, go and talk to the wizard about it instead of talking to the steward and accusing him. The wizard will tell you when the killer will strike next, and you can "catch" him in the act (and by "catch" I mean "fill with arrows").

The court wizard can usually be found in his quarters in the Jarl's residence, his room is the only one with an arcane enchanter.

Unfortunately, you can't skip ahead just by pickpocketing the guy and looking at his journal - after all, it's not that incriminating, he could be writing a story or something.