It seems to me you might have to think outside the box ... Someone has already suggested
Scout but there is a place in Lincolnshire called Scotter (meaning tree of the Scots') and
Sheila Scotter was a famous Aussie fashionista.
Or you could used Southcott or Sothcott - English surnames, not Scottish, however.
Or a Gaelic name such as
Ailsa or
Fiona or
Morag or
Sorcha and use
Scottie as the nn -- or or
Alexandra or
Flora or
Lilias which are widely associated with Scotland.