As the title says - I need to do a factory reset on my iPad Mini, but I don't want to upgrade the iOS version while doing it. Is this possible at all or will I have to make do and upgrade iOS as I am factory resetting the device?
Yes, use Cydia Impactor. It is available in the Telesphoreo repository (of Cydia), in the Utilities category.
If you have made a backup before you made the jailbreak you can do it easily with itunes.