How to backup data for Shazam app from iPhone 3GS NOTE : I just want to backup only the data associated with Shazam app, not the full iPhone backup.

Apple recently swapped my iPhone 3GS due to some issues on the speaker, but I am having issues with 3G and WiFi after the swap. When I go and visited the Genius Bar, he suggested to restore the iPhone and set it up as a New iPhone, and not to restore via a backup copy of iPhone.

But the real problem is all the existing data is lost when I do this. So I want to take a backup of Shazam app and when I setup new iPhone, I can put this data back into the app.

How can I do this ?
I think there is no way to achieve this without jailbreaking the device.

I've just checked the Apple developer tools, but they only allow you to get the content of apps that you developed yourself, not apps downloaded from the AppStore. And even with these you can only backup, but not restore :-(

I'm pretty sure it's possible on a jailbroken phone, but I have no expertise in that field, so I can't tell how.