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There might not be much of a semantic difference, but I assure you, most native speakers would choose сами or мы сами in that case.

You can easily say мы there, no real problem. Сами is there for style, you know, it's best not to repeat the same word in the same sentence. In colloquial speech people also say things like я сам...,...

нами would indicate the instrumental case, which is outright wrong, because сами is the subject of the но clause of the sentence, therefore you need nominative and a different word for that matter.