Jon,
Not to butt in, but I see both sides here. I appreciate that you recognize that Shaw was not in on a conspiracy to kill JFK. But Fred is also right. So far at least, no one has been able to find the document that the CIA historian referred to. I suspose it could be yet to be released but it appears that he was referring to a collection that is now available. And I have to assume that conspiracy-mined researches would have unearthed it by now if it existed. At this point, it appears to be an error by the historian, but I could be wrong.
If you can locate the declassified primary source document, feel free to share it. The Morley article that cited the HSCA summary of the CIA file on Shaw is from 2016. Maybe the document you're referring to was released in 2017's JFK file declassifications.
Also, not all government informants are paid and some are paid under the table. So we shouldn't assume that just because Shaw stopped being an 'on the books' informant in 1956 that his relationship with the CIA or other intelligence agencies ended that year.
Maybe Shaw did end all ties with the intelligence agencies in 1956 but I see no reason to assume that is what happened.