iPhone 4s 6.1.3 Update to IOS 6
No - you would need Apple to start signing iOS 7 for that hardware. Since Apple is signing iOS 9 it's not signing 8 and lower anymore. Basically, upgrading to anything but the latest is essentially a downgrade and not supported unless you've already jailbroken or made arrangements to fake out the code signing needed for an iOS update.

Basically, you can stick with what you have or go all the way to 9 at this point.