According to Wikitree, 2 people, including yourself, have taken the Family Finder autosomal DNA test. Both of these profiles are private
John Wilson Hay is close enough relative that autosomal testing would be better in this case, especially if you test a sister of your father, and any 2nd/3rd cousin or closer.
I was able to determine a NPE occurred when I tested a 2nd cousin on 23andme, but this alone can't determine if the NPE is on my side or my cousins. AncestryDNA found a 1st cousin, in which our trees did not connect. This narrowed down the NPE possibilities to 4 grandfathers, and Y-STR tested narrowed it down to 1.
I had tested my ySTR in 2008, and it was not until 2015, that it had any real value.