First you say the library is okay but then you say it is a nothing library which implies it is not okay. The way to avoid having to wipe a phone is to transfer the library correctly.
Moving a library: Quick answer if you use iTunes' default preferences settings: Copy the entire iTunes folder (and in doing so all its sub-folders and files) intact to the other drive. hold down the option/alt key while starting iTunes and when requested to select a library select the iTunes Library.itl file in the copied folder.
When this is to a new computer put the copied iTunes folder in the default location of Macintosh HD > Users > *User Name* > Music (or Home > Music) then you don't even need to start with the option key held down, iTunes will automatically look for it there. (Make sure there isn't anything already in the iTunes folder there that you want to keep since you will be replacing it with the one you are moving.) Remember to authorize the computer in iTunes to your Apple ID if you use this to sync to Apple mobile devices or play DRM protected media (e.g., movies).
Certain items used in iTunes related activities are not stored in the iTunes library folder but in special folders. If you are moving a library to a different computer you may wish to copy these too:
- Apple Music cache files: http://dougscripts.com/itunes/2015/09/new-flush-apple-music-cache-files/
- iOS device backups, various preferences files: https://discussions.apple.com/thread/3285925
As for the app transfer, you can't anymore with new "App Thinning" with iOS9. To make apps smaller they are being customized for specific hardware when downloaded from Apple directly to a device with iOS9. Apps downloaded directly to a device from Apple may no longer work on any other kind of device. Apple has decided there is no point in syncing these to a computer since each device should ideally get a customized version directly from Apple. If you want a backup copy on your computer you can transfer a non-thinned version directly from the Store to the computer which should you need it can be transferred to any i-device (but will take up more room).
Here's the technical description: https://developer.apple.com/library/watchos/documentation/IDEs/Conceptual/AppDis tributionGuide/AppThinning/AppThinning.html - iOS9 App Thinning > "Slicing is the process of creating and delivering variants of the app bundle for different target devices. A variant contains only the executable architecture and resources that are needed for the target device." ... "The App Store will create and deliver different variants based on the devices your app supports."
