A subclass of UIActivityViewController where AirDrop is the only sharing option. See http://cjoseph.com/post/114784061214 for a little bit more about how this came together. And rememeber: this sort of trick should really be a last resort, and could potentially break with any system update. Use it at your own risk.
Note: currently the end result is only sized for the iPhone, and you may want to add handling for devices that don’t support AirDrop before showing the share sheet.