Honestly, I see nothing wrong with "Because I said so." I'm the parent, you're the child. If I tell you to do something, you do it. If I tell you to stop doing something, you stop. You don't question. Maybe that's not touchy-feely enough, but I still feel like sometimes it's appropriate.
I'm certainly said, "You're fine." True story. My then probably 3-year-old came running to me one day holding his index finger up in the air, grasping it with his other hand. Crying hysterically. "Look, look, I'm bleeding, I'm bleeding." There's red all over the finger. Yep, he had been coloring and got red marker all over his finger. He got a big, fat, "You're fine" for that one!
And also, "There's nothing to be afraid of." Same child, maybe a year later. I'm in the shower. Boys are playing in their playroom. All of a sudden, I hear screaming, I mean SCREAMING. Child running past the bathroom into my bedroom. I immediately jump out of the shower grab something to throw around me and run into the bedroom. Child is now hiding behind my bed, yelling, "Run, run, hide, hide, duck!" I'm trying to figure out what horrible monster is chasing him through the house. Finally get, "A bee, a bee." out of him. I go looking in the playroom. Yep, a house fly. Sorry if I traumatized him, but I told him it was nothing to be afraid of. Oh, and probably threw in a "you're fine" for good measure!