My iPhone is locked down with the touchID (and thus the passcode) and when an update comes through if I choose to delay, it prompts me to do it later in the night and asks me for the password. If you enter the password, then the update will happen during that time period automatically.
If your device doesn't have a passcode, then delaying (after having begun the installation) might just cause it to install the update at that later date and not give you the option to delay it further.
Generally, if you don't intend to update for some reason, it is best to just ignore the Software Update section entirely because that process HAS to be started manually and it will not nag you.