What you are describing isn't a koan, it's a parable or saying. The latter can be appreciated and rationalized by the discriminating mind. Koans, on the other hand, are something entirely different. In order to apprehend what koans are pointing at, discriminating thought must be abandoned. Parables have meaning that can be conveyed. Koans are objects that can be observed. Parables are a recipe for rice pudding. Koans are the taste of that rice pudding.
But to answer your question, that phrase doesn't appear in any of the major koan collections. But here's something similar. This koan doesn't tell you not to worry. If you dive deeply into it, it will show you how not to worry:
Mumonkan - Case 5: Kyogen's "Man Up a Tree"
Kyõgen Oshõ said, "It is like a man up in a tree hanging from a branch with his mouth; his hands grasp no bough, his feet rest on no limb. Someone appears under the tree and asks him, 'What is the meaning of Bodhidharma's coming from the West?' If he does not answer, he fails to respond to the question. If he does answer, he will lose his life. What would you do in such a situation?"
Even if your eloquence flows like a river, it is of no avail. Though you can expound the whole of Buddhist literature, it is of no use. If you solve this problem, you will give life to the way that has been dead until this moment and destroy the way that has been alive up to now. Otherwise you must wait for Maitreya Buddha and ask him.
Kyõgen is truly thoughtless;
His vice and poison are endless.
He stops up the mouths of the monks,
And devil's eyes sprout from their bodies.