Download arbitrary file with Google Chrome
Right click the link and click "Save Link As..."
EDIT: To follow up on the need to download arbitrarily from clipboard, I would just create a generic HTML file and use the above solution. Save as mylink.html to file system somewhere. Open in Chrome.
<html>
<a href="http://www.mycompany.com/secretvideo.mp4">Link</a>
</html>