Go with the documents. Those document not only his legal name, but also his father's intent in his naming, as well as the name your father himself used. I am a Junior, and I would find it very condescending and offensive for someone else to assume to know better than me what my name is or should be.
Also, as a Junior, it is my opinion that the purpose of the Junior suffix (or, alternately, "II.") is to indicate someone, usually a son, who otherwise has exactly the same name as their father or another close relative of a prior generation (who didn't have a generational name suffix himself). If there is some other differentiating element in their name, "Junior" is not necessary.