Apple - Disable iCloud Backup without deleting existing backup?

If you turn off iCloud Backup on your iPhone, the iCloud Backup isn't deleted from your account immediately.

The Backup does get "abandoned" some time after it stops receiving updates, I think it's like 6 months... but you should call up a AppleCare rep to confirm what time frame it is, I never found out how long, just that it is months afterward the backups stop from that device

Short answer

Since you've clarified that what you're really trying to achieve is a downgrade from iOS 10 to iOS 9, I'm sorry to say there's no way to re-install iOS 9 on your device. Basically, when a user installs a different version of iOS on their device, the process involves Apple signing the installation. Unfortunately, Apple stopped signing iOS 9 installations in October 2016.

For more info see this answer.

Long answer

If you do a full iTunes backup, it's not creating a disk image. Instead, it's a backup of your data, such as text messages/imessages, notes app data, map locations, call history, favourite contacts, various settings, third party app data, and so on.

If you've enabled the encrypt backup option in iTunes, then additional info can also be backed up (such as Wi-Fi settings, saved passwords, health data, etc). However, in no scenario is it backing up the OS itself.

If your backup was made while you had an earlier version of iOS installed, all your data can still be restored onto a device running a newer version of iOS, but the OS itself will not be downgraded to the version you were running when you made the backup.