Mozilla's send.firefox.com lets you send an encrypted file privately to anyone else, providing an automatically-expiring link.
It supports files up to 1GB, and after uploading something, it'll give you a link to send to someone else. That link will expire once they've downloaded it or once 24 hours have passed. So someone else's procrastination is really your biggest limitation here. Files are also encrypted as they're uploaded, and Mozilla says it "does not have the ability to access the content of your encrypted file."