Take the south coastal road, not taking the Ness Road, go as far as the Frustigarth Road and take that. The stone is in the second field after Cot on the Hill, don't be tempted by the first field as it is rather boggy. I went to have a look at the wartime building on the other side and found what could have been an outlier. Didn't measure it but say a metre square with another stone underneath
To the eastward of this little wart or ward-hillock, about an English mile, is a high stone, called the Standing Stone of Shapinshay. Above the level of the ground it is 12 feet high, and perhaps 5 or 6 below it; its breadth is between 4 and 5 feet; its thickness a foot and a half; and from its being clothed in moss or scurf, it has a very venerable majestic aspect, and seems to have weathered many ages. In form and dimensions, it very much resembles stones that are found standing in many of the other islands, particularly, the circle and semicircle in the parish of Stenness..
The RCAHMS record adds: "The stone occupies a small patch of unimproved moorland near the highest point in the SE part of the island. A few years before 1928 it was overthrown and re-erected, losing a portion of its upper part in the process. " So it's only 2.9m tall now.
This piece (on p80-1 of the New Statistical Account of Scotland, vol15 - 1845) mentions another stone:
"Towards the north side of the island, and by the sea side, is another large stone, called the Black Stone of Odin. Instead of standing erect, like the one above mentioned, it rests its huge side on the sand, and raises its back high above the surrounding stones, from which it seems to be altogether different in quality. How it has come thither, for what purpose, and what relation it has borne to the Scandinavian god with whose name it has been honoured, not only history, but tradition is silent."
So possibly natural? But interesting for the name.