Hi, ehbox,
most computers can't open an SWF by itself, as the Adobe Standalone Flash Player is not installed. You cannot download it, you only have it when you have Adobe Flash Applciation or Quark Interactive Designer or QuarkXPress 8 installed.
So you either need to advise your client to drag the SWF into an open Browser Window or you need to create a projector.
I am puzzled as why you do not get a file when creating a projector. You get a Save Dialog right?
Thanks
Matthias