I didn't interpret General Order 24 as some sort of Death Star weapon. But it only took the Enterprise 15 minutes to identify all potential targets, so Scott seemed prepared to carry out the order if the hostages weren't released.
The Eminians had previously destroyed a starship, had attacked the Enterprise, and two landing parties (including Fox and his flunky) were being threatened with execution if the Enterprise didn't surrender. Normal diplomatic negotiations had failed. Kirk was out of options, until one presented itself just in the nick of time.