What about email? Android Beam? Cloud hosting solutions such as Dropbox or Google Drive? If the app could not only send data that way, but offer to handle said data when you attempt to open it from whatever source, that would be great (assuming it doesn't already behave that way - I should probably mention I haven't had a chance yet to play with the app and see for myself what kind of functionality it has...).
On a related note, I'm not sure how successful you'd be porting this to iOS - but if you were able to, AirDrop and Continuity would fit very well in this app.