Clarification of shika

I was taught that 「しか」means the same as 「だけ」, differentiated only by the fact that the former is negative and the latter is positive. I've been thinking this whole time that しか literally means "except for", and it made sense to me for years. But is that right?
e.g. I would translate 「今日ケーキしかたべなかった。」to literally mean "I ate nothing but cake today."
But by that logic I could say 「日本しかどこにも行きたくない。」
Can someone please clarify this? And can you explain why if I'm wrong? Sorry for the long question.

「今日ケーキしかたべなかった。」to literally mean "I ate nothing but cake today."

Correct.


「日本しかどこにも行きたくない。」
Not quite. You can say 日本しか行きたくない。to say "I don't want to go (anywhere) but Japan."