Provide the ability to share a file one time to an email address, with a link and secured with a pin maybe. No need for the receiver to go through the sign up process, and the file is not exposed publicly. After the receiver has downloaded the file, the link then becomes invalidated.
I think something like a "download access time after the first download" would be good as well. So as soon as the download link is requested for the first time, the file should be available for X minutes for restarting the download, in the case that the Internet connection breaks while downloading. With this option, the user could restart the download as long as the X minutes have not expired.
A PIN would be an option to enhance security, so to stop interception type access attempts. The PIN could be shared by any medium the sender wanted, such as a phone call, sms, separate email, carrier pigeon...The one time download would be ok, but having some anti-interception measures (such as pin) would also be a great addition.