I don't know if such a soundtrack is available on its own but you can check out the Robert Wise DVD commentary. It has the music track without the singing (like karaoke). The commentary is intermittent and he doesn't speak during the music, so it may be what you're looking for. If it suits your purposes, you could extract the desired DVD audio track (with a program such as FlaskMpeg) and then do what you like with it (e.g. divide it up into tracks of your choice).
Also note that the 40th Anniversary Edition CD available in the UK (e.g. Amazon UK) has extra orchestral tracks not included in the US version, such as the My Favourite Things/Salzburg montage.
Hope this helps! :)