I think the Kirk Sessions are the way to go forward (if only to discount John Skinner the school teacher

)
I think there is a good chance that this is Ann Ross and family considering the addresses. I notice that your John had a son named George who registered the death. John Skinner senior's occupation is given as Farmer and not Farrier on the death entry.
If you have a look at them on FREECEN you can view their neighbours
1841 -
Piece: SCT1841/252 Place: Banchory-Ternan -Kincardineshire Enumeration District: 2
Civil Parish: Banchory Ternan Ecclesiastical Parish, Village or Island: -
Folio: 2 Page: 7
Address:
Burn Of Bennie
Surname First name(s) Sex Age Occupation Where Born Remarks
ROSS George M 40 Ag.Lab Outside Census County (1841)
ROSS Ann (Mrs) F 40 Kincardineshire
ROSS Margt F 9 Kincardineshire
ROSS Jean F 7 Kincardineshire
ROSS George M 3 Kincardineshire
ROSS Ann F 1 Kincardineshire
ROSS Ann F Unknown Female Servant Kincardineshire Age not enumerated.
1851 -
Piece: SCT1851/252 Place: Banchory-Ternan -Kincardineshire Enumeration District: 8
Civil Parish: Banchory Ternan Ecclesiastical Parish, Village or Island: -
Folio: 198 Page: 1 Schedule: 1
Address:
Woodend
Surname First name(s) Rel Status Sex Age Occupation Where Born Remarks
ROSS George Head M M 53 Stonedyker Farming 4 Acres Aberdeenshire - Aboyne
ROSS Ann Wife M F 51 Kincardineshire - Banchory
ROSS Ann Dau U F 10 Scholar Kincardineshire - Banchory
ROSS Isabella Dau - F 8 Scholar Kincardineshire - Banchory
ROSS Ann Sister U F 45 Pauper Formerly Servant Kincardineshire - Banchory
BURNETT Jane Visitr U F 15 Farm Servant Kincardineshire - Banchory
Regards,
Annette