IPhone 5c :: Applying Backup Of One Device To A Different Device?

This past week, my phone "fell" and the screen broke beyond all repair. And I'm not talking about a crack...I'm talking about a huge crack as well blue lines being displayed whenever I hit the home button. Other than that, the phone still works. It charges, it syncs, it vibrates when I get calls or messages but I can't see anything on the screen. I know that I can still unlock though. I managed to backup my pictures directly onto my Mac using iPhoto. Besides my pictures and Calendar dates, there wasn't much that I cared for within the actual phone.Â

I went to my local phone service provider place and they told me that since my phone was a 4S and was covered for damage, I could send it to Apple in exchange for a new phone. I already contacted them and received my new 5C. Now, I'm not really worried about the pictures because they're already in my computer; I'm worried about all the Calendar dates that are in my broken 4S. Yes, I did do a backup AFTER it fell so I have a backup ready. But the thing is that I do not wish to sync this onto my new 5C just for the calendar dates. Â

I have an old iPod 4th Generation that I'm willing to use to restore with the backup of my 4S but I don't know how to do that. I was hoping that I could apply the backup of my 4S onto my iPod and then manually enter all the dates that I needed onto my 5C.