First off be sure to scroll down that window of choices (Camera, Camcorder, Music Player, etc., etc.) to see your other options. If you also keep your resume in your Dropbox or Google Drive those options will show also. If you have a file manager app like 'ES File Explorer' on your phone (highly recommended BTW), that will also be showing as an option. In that case just use ES to navigate to wherever you have your resume stored on your phone and select it that way.
Regarding the docx suggestion, I just want to point out that while MS Word is definitely the dominant word processor out there, using pdf does have some advantages. A pdf will keep it's formatting and appearance the way its creator intended, there is higher degree of likelihood it will appear exactly the same on different computers, while doc and docx files are tied to years of multiple versions and compatibility packs of MS Word (with numerous backward and forward compatibility issues due to Microsoft's love of vendor lock-in) along with the inherent problems of different operating systems relying on different sets of fonts.