Worst case 6.1.4 is still signed so you can simply download it from Apple for your device (you can find the direct download links all over) and then do a Option + Restore click (OSX... I think it's shift in Windows but not 100%) and choose the file you downloaded.
KEEP IN MIND: You cannot restore a backup from iOS 7 to iOS 6.1.4. So your iCloud stuff will come back fine, but your local stored stuff cannot go back.
So if you have pics, etc, you want to save make sure you either:
a) Copy them to the computer first
b) Update your replacement phone to iOS 7 and restore your previous backup
Before I restore, since I tend to like fresh installs out of habit, I always use Preview in OSX to copy all my pictures to my Macbook Pro so my paranoia of losing them is taken care of.
Best of luck.