"Ko" doesn't seem as unintuitive of you consider usage of "tonight" in English, i.e. "Let's meet at 10 tonight." Not exactly the same usage as "at", but makes Hindi grammar less frustrating for me here. =)
"ko" is used when stating the time of something, rather than translating the English "in." Literally, it's like "at the evening."
As for shaam, it sounds to me like the normal word. Jaagna is wake up, verses uThna = get up.
Just so you know, your proposed sentence is not wrong. The sentence in the answer is comparatively better. Your sentence looks correct to me as a native Hindi speaker and everyone will understand what you mean to say.