Restore iOS 10 backup to an old iPhone 4s I just broke my iPhone 5s running iOs 10.1.1 and I would like to restore a back-up to an old iPhone 4s that I own.

iTunes claims that the iOS version is too recent to restore it. Is there a way to tweak/downgrade the backup in order to avoid using the iCloud backup?
You can't restore a backup of a newer iOS version to an older iOS version.

However, you can examine the contents of the backup using iBackupBot and then manually restore what you can using iBackupBot's restore mechanism. This won't restore incompatible databases such as your messages, but you can usually restore app data.