I dot think you'd be charged with destroying evidence, because that would be assuming that there would be evidence. Instead, I suspect you'd be charged with contempt or obstruction of justice, or something along those lines. Otherwise, yes, I think you're right.

Under civil law, a finding that evidence was destroyed implies a finding of the fact that the destroyed evidence would have supported. I'm not sure how this would affect a criminal law proceeding, though I'm reasonably the prosecutor would be allowed to introduce that fact to prove guilt. (Ultimately it would be up to the jury to decide.)