Thanks Sven, I was actually going to pull up this thread myself for a different reason, but I'll get to that later.
Somewhere I have an account of the course from July of 1892 which indicates the course was 9 holes and lists hole yardages as identical to the Davis's original 9 hole course. In 1892, John Cuthbert was the professional at Shinnecock (more on this later.)
Then Dunn arrived in the spring of 1893, and laid out his 12 hole course. Dunn's course was not just an addition of three holes. His 12 hole course featured 8 new holes and included only four holes in the same approximate locations as Davis's 9 hole course.
Mike Cirba implies that maybe it was Davis who built the 12 hole course, because "certainly being located in Newport in those years he wasn't all that far away." There is no contemporaneous evidence indicating that Davis ever returned to Shinnecock to replace his original 9 hole course with a 12 hole course.
And Davis was not even in Newport in 1892. He was the professional at Royal Montreal. According to Davis, while he did visit Newport in November in 1892, he did not begin work there until March 1, 1893. In late 1893, Davis wrote of his early history at Newport and his encounters with Dunn, but he made no mention of returning to Shinnecock to revise the course, and, notably he did not take credit for the design at Shinnecock.
Dunn was hired at Shinnecock in the spring of 1893, and he reportedly lengthened the course that spring. Many years later, Dunn described having built the 12 hole course, "I laid out plans for twelve holes and started work with one hundred and fifty Indians from the reservation . . . ."
If there is any contemporaneous evidence that Davis designed and built the 12 hole course, I've never seen it.