Between an iPhone, iPad, and Mac, AirDrop moves a file with no email or cloud in between. Open the Share menu, pick your format, choose AirDrop, and tap the nearby device.
 
It works with every format: iReal Pro charts, PDF, MusicXML, MIDI, audio, and a playlist's setlist. AirDrop is an Apple feature, so it is not on Android or Windows.
 
For more, see Share a song or playlist on the iReal Pro website.