Howdy Glen Bervie,
I too have a hockey sock full of Walkers starting with my great-grandmother in Greenock and thence over to Kinkardineshire as Millers.
My ggrandmother was Mary Jane W. born Jul 5 1846 in Markinch, Fife and was married to a Guthrie from Greenock.
Her parents were Alexander W. married to Catharine Lyall.
They go back further to connect to Brands, Blackies and Officers.
If you see any traces give me a shout,
Gord