Scotcher/Stuart Link

Hiya,
I'm researching my ancestors who were in the last 2 or 3 centuries Stuart and Scotcher from different families.

All I know is that Scotcher derived from a Stuart(s) who escaped to France from Oliver Cromwell with King Charles (2nd?) and as it was not wise to be known to be a Stuart they became known as La Cher Scot - later Scotcher. - does anyone know more about this and who they were/are as all I have is word passed down in the form of letters.

I have a Bena who was a Scotcher related (aunt) who told the tale to Billy (Llewellyn) Bullock Webster in a letter and the storey has been passed down through her family and down through mine.
She was related (step?/sister?) to my Gt Gt Grandfather Edwin Stanley Clark - (nicknamed D'Orsay) of Chelsea London in the 19th C.

Does anyone know the names of any early Scotchers? and links to Stuarts? or any info that might help?
thanks
regards
Amanda