Bill,
There were a lot of great Willies in golf. Davis, Dunn, Dow (Scotland), Dow (MA), Park, Park, Jr., etc.
Willie Davis arrived in Southampton in 1891 and laid out the first 12 holes at Shinnecock Hills. The holes were completed in a relatively short time and were fascinating examples of the geometric era. Sometime later the course was becoming congested and a nine hole course, the Red Course was laid out for the ladies. This is probably the origin of the color red for most forward tees. After a short time, the two course concept was abandoned and a single 18-hole layout was put into play around 1893.
Willie Dunn came to town in 1895 and did some redesign work, lengthening the course to over 5000 yards.
Five holes from the Dunn/Davis routing were on land to the West of the Clubhouse. The 5th was near the site of the subsequent Macdonald 1st. The 15th was near Macdonald's 12th. The 17th near the site of Macdonald's 16th. The 18th green might be on the site of the Macdonald 18th green.
Some remnants of the old holes to the east of Tuckahoe Road can still be seen among the short course built for children and newcomers to the sport.
Nothing of the original 12 holes exist today. For that matter, there is essentially nothing existing from the Macdonald version of the course either. Some confusion may lie in the fact that Flynn was instructed to redesign the course while keeping 18 holes in play at all times. This led Flynn to build 12 new holes and then gradually phase out six of the existing ones with play shifted to other pre-existing holes while Flynn finished the complete remodeling. While a few greens sit on the same site as Macdonald's greens, all the greens, tees and bunkering are Flynn. The hole that is closest to the Macdonald version is the current 3rd, Macdonald's 13th. The Flynn tee is to the left of the par 3 2nd green, Macdonald's tee was on the right side (the site of Macdonald's par 5 12th) near the forward tees but some of the bunker locations and the greensite are located on the same sites. Flynn's green was larger than the Macdonald green (it is going to be expanded from its current size) and the bunkering far different in look and scale.