DevExpress offers a free coding assistance tool called CodeRush Express which offers this refactoring. Here's a link to the page showing the refactoring.
I own a license to their full-blown CodeRush w/ Refactor Pro, and I love it.
EDIT
Following the edit of the question, I just wanted to add that I'm able to do that refactoring using the following keystrokes (with the cursor on the name of the nested class)
- Ctrl+` (opens refactor menu)
- Enter (or arrowing down to the option if it's not already selected)
That automatically creates a new file in the project with the name of the nested class as the name of the file, moves the nested class to that file, removes it from the original location, and drops a marker at the place where the nested class was removed. Hitting Esc takes you back to where the extracted class was removed.
It is a huge time-saver. Granted, my day's not full of extracting nested classes, but it's an example of how saving a couple of minutes here and there can really help remove the friction from some common development tasks.