Hello roycymru,
I wonder whether you have proceeded further with this search?
It looks as though Mary (CHEYNE) DUNBAR is rather older than you thought ...
From the IGI, a Charles DUNBAR married a Mary CHEYNE in Lonmay in 1803. From the IGI, children b Lonmay with father Charles DUNBAR (mother's name is not recorded unfortunately) are Charles 1803, Mary 1805, James 1808, Robert 1810, Margaret 1812, William 1817, Barbara 1819, Catharine 1821 and Cumine 1824 (I note from the IGI that Thomas YULE & Catherine DUNBAR named a child Cumine).
From FreeCEN, in 1841 in Lonmay there's a Charles DUNBAR 68, Mary 58, Cumine 16, Mary 15 ... And in 1851 Charles is 79 and Mary 69, both b Lonmay. So it looks as though you may be lucky enough to find that either or both may have survived into the time of Statutory Registration!
A free search on SP, refining parameters, reveals the following:
A Mary DUNBAR, other surname CHEYNE, died age 78, in 1861 in Lonmay
A Charles DUNBAR died age 87, in 1858 in Lonmay
HOWEVER ...
Perhaps a lot of the work has been done for you

A Google (I Googled for Dunbar + Balearn) finds the following site:
http://www.rootsweb.com/~cheyne/200705-p/index.htmIt includes Thomas YULE & Catherine DUNBAR and descendants and ancestors.
Have fun,
JAP