Download large file to selected location
According to Apple Support, you can change the default Download directory in Safari:


  If you like, you can change the default folder for storing downloads
  by using your browser’s preferences. To specify a different folder in
  Safari, choose Safari &gt; Preferences, and then click General.


You should then be able to switch to use your external HDD by default.

As other posters have noted, Firefox and Chrome can also be configured to use a different download directory.

It might be possible to directly save a file (if a link is provided) by right clicking and selecting the Download Linked File As... option. Select your desired location and save the file.