Are you sure you have the shockwave flash player plugin installed for safari? You can look under the help menu -> Installed Plug-ins then scroll down the list to see if it is there. If not, go to
Macromedia to get it and then recheck using the above instructions. I'm not sure this will help. I just checked my machine and cannot play swf files in Safari either and I do have the plug in installed, but I can play them using quicktime. I might add that I'm using quicktime pro. I don't know if this matters or not. Have you tried double clicking the files and letting the default application try to play them? You can also right click or control click the file and select open with to select a specific application to use. I didn't know you could drag a file into quicktime. I have never tried doing that. Good luck.