I think the birth date of 26 April 1806 mistakenly came from a Baptism Record (Reg # 088/ 10 19. Page 19 of 165) for a William MacLeod, baptised on 27 April 1806, son of Donald MacLeod of Bayhead, (which was part of the town of Stornoway). This would not be William's Birth/Baptism Record because: (1) this 27 April 1806 baptism record says the father's name was Donald but William's parents are named on his Death Record as Kenneth MacLeod and Catherine MacIver; and (2) this baptism record says the father Donald lived at Bayhead, which was part of the town of Stornoway, while William's father Kenneth and his family lived on crofts at Back and Vatisker.
William's year of birth would be around 1803 or so, because that matches the ages on his death record and census records. I couldn't see any records on the ScotlandsPeople Index that looked like William's baptism record.
The 1851 Census says his place of birth was Back, Parish of Stornoway, Ross-shire.
The Croft History of Vatisker says that William originally came from Back (Am Bac in Gaelic). He then moved to 7 Old Vatisker, and when the crofts were redistributed in 1850, he moved to 25 Vatisker, which is the last place he was recorded as living.
"Croft History - Isle of Lewis, Volume 29" by Bill Lawson for Comann Eachdraidh Sgìr a'Bhac. (This is the Gaelic for "Back Historical Society. The Volume deals with the village of Vatisker, Gaelic form Bhataisgeir.)
I have a copy of the 1851 Census and the 1806 baptism record.