The resulting secret value (the list of filenames to show the concatenation order) would take up more space than the original file. You'd be better off simply using a one-time pad, and keeping that secret... or even keeping the original file secret directly.
Your method would work in most cases, in the sense that anyone who possessed the randomly-named single-byte files but not the secret value would be unable to reconstruct the original file... but the task of keeping the secret value secret would be more difficult than the task of keeping the original file secret, and there would still be some possible attacks on the unordered list of bytes if the original file's structure was very predictable. You would also have to be careful about how you choose your padding, since a poorly-chosen padding method could make the file structure more predictable.