Hi
I came across your post while doing a search of when the old Stranraer High School was demolished
( couldn't find anything ). 
The Ryan Centre now appears to occupy the site of the High School. 
My family moved to Stranraer in 1963, and I attended Rephad Primary.
As far as I was aware at the time, there were 3 primary schools in operation in Stranraer...,
Rephad, Park, and Sheucan.
In 1964 I started secondary education at the High School.  
My father taught at the Academy. It was definitely a secondary school at that time. 
I'm unsure what building he taught at. 
Next door to the High School was the building called the Academy Annexe.   As I recall, it was white, in a modernist 1930's style. Rather similar to the building there today ( the same one ? ). 
In 1965, pupils of the Academy, and the High School, moved to the new separate Academy and High Schools out at London Road/McMasters Road. Between the school complexes were gym/PE buildings and a swimming pool.  
My family moved away in 1969.  In 1970, the schools were renamed under the one title of Stranraer Academy. ( and went comprehensive ? )
Hope this helps