If you use the GoodReader app, you can save files to its iCloud folder (if you've enabled it) and and generate shared links for emailing. It's a fairly recent addition to GoodReader's features.
The process is kind of convoluted, but works.
First you have to get the file into GoodReader and copy it to the iCloud folder. There are a multitude of ways to do this.
Then you go to the iCloud folder, choose Manage Files from the right column, select the file, and tap the Publish button. This generates an email with the link in it. You can either use this email or copy and paste the link to some other app. It's not a direct link, but one of the secure style ones that does not show the file name. Because of that it won't work to upload stuff to sites.
When you receive the email and click on the link it opens a browser, goes to iCloud.com, and downloads the file. This works fairly well for a computer, but is less convenient on an iOS device. Strangely this aspect of icloud.com does work in Safari on the iPad, but because it does the download in Safari it has all the inherent awkwardness of doing downloads in Safari on the iPad.
