It seems all these three versions are in use: "the shadow of a doubt", "a shadow of a doubt", and "shadow of doubt", as suggested by Google Dictionary and Google search results. Google Dictionary (partially from the ODO):
the slightest trace of something.
"she knew without a shadow of a doubt that he was lying"
"she knew without any shadow of doubt"
I have always thought "doubt" should follow an article, but strangely the article-less version seems more popular according to Ngram. Any difference in meaning? Or is this a BrE/AmE difference?