This gives them the ability to download the file and save it for a later date, how can I disable that feature in Moodle?
I was looking for the same thing and came across this post.
Seeing there was no solution, I looked for it myself and a work around I found is to edit the language file resource.php in the lang directory and set the the directlink entry to blank:
$string['directlink'] = '';
I don't know if this is good enough for you.