DrDealgood
Superstar
He says both of them first, but then says "at least let me take Shireen" after Stannis rebuffs.
Again it may just supposed to be foreshadowing for the viewer, but in this scene Davos comes off as a man afraid to leave Shireen with Stannis and the Red Woman. A man who knows that there's some ulterior motive for Stannis insisting Davos go and not anyone else.
He definitely is afraid, and has been for a long time. The reaction shots for many episodes show that and are constructed for that effect. That's why his realization could be so painful, because he'll see how he wondered if Shireen was safe, and decided every time that it was unthinkable Stannis would decide to harm her.
Mane I'm all kinds of fukked up with these feelings again. This was my Red Wedding (show version).