When iMovie 10 updates files it does not affect the imovie 9 (or earlier) projects and events folders so you can still use the old version of iMovie.
I believe that earlier versions at least back to iMovie 6 will still run under Mavericks but I'm not sure which is the earliest version that iMovie 10 can update. There is no danger in trying.
If you still have the old iMovie application are you sure you don't also have iDVD? The update to Mavericks does not delete it.
If you still have the DVDs you could also consider just duplicating them. See for example: http://www.wikihow.com/Copy-Your-DVDs-With-Mac-OS-X