Welcome to the County of Sutherland Board. (Are you Roy?)
The census extracts in my file, after 1841, have as the headings of the 3rd-last and 2nd-last columns "Parish" and "County". 1841 shows "Parish" only. What county is shown in 1851 and 1861?
There was only one baptism recorded in the register for Durness in 1809: Oct 18 ; father Richard MacKay, weaver in Durin (i.e. now the village of Durness) mother Catharine MacPherson.
There was one other in the West Moine Mission on Jan 30th: father John Mackay, alias MacHeorish (i.e. son of george), Hunleam, and Barbara MacKay, Braeskill, not born in lawful wedlock.
There was a Hugh baptised 11 Mar 1808; father Hugh Mackay Shepherd in Borly; mother Christian macKay, both from Strathy
There were no Hugh MacKays baptized in 1810.
Odly, all of theIGI entries for Janet Budge were submitted by LDS members (no extracted entries) Her marriage to hugh in 1833 and the birth of her children (John 1834; Hugh 1835; Donald & James 1838; and Janet 1840. There were 3 members submitting. Perhaps you could try contacting them?
Of the Durness Hughs, the West Moine entry seems slightly more promising because it is located closer to Latheron and because the father's name was John, the name Hugh gave to his first son.
Good luck,
Ian