I have had to do this for a client as well, and the way I did it was to upload the file to Google Drive (could be your cloud storage service of choice), and then get a share link. Be sure it is not a restricted sharing link, but rather an open-to-the-web link.
Create a button in a link block, and style it to your liking. Then copy and paste that share link into the link block settings. That way, when you click on the button, it links to the Google Drive file, and they can view or download from there.
Hope this helps! 