Umm... no internet = no DropBox
OP, I've looked around and am not sure what you want to do is possible. Even if you copy the app to a thumb drive and mail it to your friend, there are probably dependencies required for the app that are installed by the app store that won't be on your friend's computer.
App Store apps usually have to be authorized with the Apple ID and password of the purchaser to work on another computer. An internet connection would be necessary for that.
Maybe someone else will know more.