As you have found, unfortunately, it's not possible to attach anything other than a picture while in the Mail app. However, have you looked at the options in the app that you are using to view the PDF file? A lot of these apps have an option where you can send an e-mail directly from within the app. It'll use your default Mail address to do it...
Or, another suggestion is to upload the PDF file to a cloud storage (such as Dropbox), make a link to it and then e-mail the link. This often is easier/better because the recipient doesn't have to download a huge file right away in their mail.
Just some ideas.
Marilyn