I dont know about the worthy project, but offer the following
there are several hundred Williamson in the times the of the best known famine ie1846-1851 the website
www.familysearch.org has a record of those leaving Ireland crossing the Atlantic ocean at that time. those travelling to Scotland are not registered that way or any way.
Looking at John Williamson b Ireland in the Scottish Census 3 born Ireland in 1841, 15 born Ireland 1851, 9 in 1861 census. Have you identified him in these census. his wifes maiden name might be important if known and family children listed as born in ireland
Searching for John Williamson b Ireland if he arrived in Scotland at an age, that would relate to him being born before 1816-1821 He himself might be listed in Irish Tithes Applotment books 1823-1837.his minimum status for himself or father to be having homestead house valued at 5 shillings pa to be included. Otherwise if you cant connect to a parish and then church record you are almost out of luck.
If you have a definite early ID in Scotltand please help us by telling us.
Irish Tithes Applotment books 1823-1837
website for 26 counties gives 8 results
http://titheapplotmentbooks.nationalarchives.ie/search/tab/home.jsp the index of the Irish Genealogy Hub
http://www.irishgenealogyhub.com/gives 31 entries [none listed for Co fermanagh. including duplicates as follows
Williamson, John Townland: Carntall Year: 1835 Ballylinny Antrim
Williamson, Jno. Townland: Carnany Year: 1825 Ballymoney Antrim
Williamson, John Townland : Drumlee Year: 1834 Finvoy Antrim
Williamson, John Townland: Ballynabarnish Year: 1833 Templepatrick Antrim
Williamson, John Townland: Craigarogan Year: 1833 Templepatrick Antrim
Williamson, John Townland : Aghantaraghan Year : 1830 Ballymore Armagh
Williamson, John T: Ballytrodden Y: 1833 Clonfeacle Armagh
Williamson, John T: Derryscollop Y: 1833 Clonfeacle Armagh
Williamson, John Townland : Blockery Year : 1828 Drumcree Armagh
Williamson, John Townland: Drummond Year: 1834 Kilclooney Armagh
Williamson, John Townland: Mullochglass Year: 1835 Killevy Armagh
Williamson, John Townland: Mullochglass Year: 1835 Killyman Armagh
Williamson, John Townland: Kilmakenty Year: 1833 Kilmore Armagh
Williamson, John Townland : Anasamry Year : 1828 Loughgall Armagh
Williamson, John, Jr. Townland : Anaghmore Year : 1828 Loughgall Armagh
Williamson, John Townland : Drummond Year: 1834 Mullaghbrack Armagh
Williamson, John Townland: Moneybranon Year: 1832 Aghadowey Derry
Williamson, John Townland : Ballymaglin Year: 1825 Aghanloo Derry
Williamson, John Townland: Killeyvalley Year: 1822 Desertoghill Derry
Williamson, John Townland: Alterbryan Year: 1828 Dunboe Derry
Williamson, Jno. Townland: Killymuck Year: 1833 Tamlaght O Crilly Derry
Williamson, Jno. Townland: Carnany Year: 1825 Ballymoney Derry & Antrim
Williamson, John Townland: Loughadian Year: 1828 Aghaderg Down
Williamson, John Townland: Ardglass Year: 1833 Ardglass Down
Williamson, John Townland: Ballycowan Year: 1829 Drumbo Down
Williamson, Jno. Townland: Ballynagarrack Year: 1834 Tullylish Down
Williamson, Jno. Townland: Ballynagarrick Year: 1834 Tullylish Down
Williamson, John Tl: Mullinahorn Yr : 1837 Aghaloo Tyrone
Co Cavan
Williamson John Carrickmore Killinkere Cavan 1833
Co Donegal
Williamson John Gortavern Tullyfern Donegal 1830
Williamson John Cratlagh Tullyfern Donegal 1830
Williamson John Kerrykeel Tullyfern Donegal 1830
Co Monaghan
Williamson John Aphernaugh Aghabog Monaghan 1833
Williamson John Corrigary Ematris Monaghan 1830
Williamson John Killigowan Killeevan Monaghan 1825
Williamson John Tyrafinog Monaghan Monaghan 1826
I think you said the North of Ireland I have given you the 9 counties of Ulster covered sadly in a biased incomplete Tithe record but still a great help