Here's a relatively simple approach...
Create a new blank sequence by clicking the + sign to the right of the sequence 1 tab that's above the timeline.
Click the sequence 1 tab to restore it to the timeline.
Either select (highlight) all the clips to be used for the shorter video or split out the segments to be used and select each, one-by-one.
Press <ctrl-C> to copy them.
Click the sequence 2 tab.
Press <ctrl-V> to paste.
You can then work with sequence 2 to refine the abridged version. When complete, and while it is on the timeline, export it. ONLY the displayed sequence will be exported.