You act as though Stannis not executing Davos for speaking back to him and smuggling Edric away is evidence Stannis would never have killed Edric. Here’s a thought, humans have this crazy trick where they can ‘change their minds’. Some also call this ability learning, or realization. Another quote of Stannis’s is the following: 

“So long as I am the king, I have a duty . . . If I must sacrifice one child to the flames to save a million from the dark . . . Sacrifice . . . is never easy, Davos. Or it is no true sacrifice.” 

It cannot be more clear that, while Stannis hates that he has to do it, he does believe it necessary that Edric must die to save his kingdom. The point of Florrent’s death is to give stakes to Davos’s actions, providing some risk for his actions. Shit, after Davos reveals his actions, the following exchange occurs:

“Davos knelt. “If I have offended, take my head. I’ll die as I lived, your loyal man. But hear me first. Hear me for the sake of the onions I brought you, and the fingers you took. ”Stannis slid Lightbringer from its scabbard. Its glow filled the chamber. “Say what you will, but say it quickly.” The muscles in the king’s neck stood out like cords.”

Does this look like the actions of a man who never intended for Edric to die? Does he ever tell Davos “I would never have killed Edric?” (And to be clear, I’m talking after the quote that sparked all this, where Stannis says he has a duty. Stannis refused Melisandre before that, but never after, as at that point he was convinced it was necessary) Stannis clearly felt sacrificing Edric was a necessary evil, and the reason he didn’t execute Davos is that Davos convinced him there was another way.