I think Phantom of Venice would be a good game to speedrun, except for the mosiac puzzle, which is about seven minutes that you can't skip. Most games in the Nancy Drew series have one or more puzzles like that which frustrate speedrunning.
The best Nancy Drew game to speedrun is probably one of the earlier games, like Nancy Drew: The Final Scene. In the earlier games, you can turn off the voices and the closed captioning. This allows you to skip straight through all phone conversations, because the game doesn't have text to display or sound clips to play.
Then again, I imagine something like Nancy Drew: Last Train to Blue Moon Canyon would be easy to speedrun, because it's a straightforward game, and a lot of the plot is totally optional.
I won't be trying a speedrun soon, because I'm busy with other things, like my Phoenix Wright playthrough. Speaking of which, there are more videos!
Video #14: Phoenix begins the second day of investigation. Pearl is keeping secrets about what she was doing at the time of the murder, so he decides to investigate that.
Video #15: Phoenix sees Morgan Fey being creepy and generally suspicious. He also visits Maya in prison.
Video #16: Phoenix gets Pearl to confess what she was doing at the time of the murder. She broke an urn with a ball and was trying to fix it before anyone noticed.
Video #17: Phoenix goes to the hospital, where he meets a creepy pervert who knows all about Ini Miney.
Video #18: Phoenix, using the information from the pervert, is able to undo Ini's psyche lockes and learn her secrets. She is most likely the real murderer.
Video #19: Phoenix goes over everything with the Chief, to prepare for the trial.