Bit more on this dong-dang William Chancellor of Scotland that everyone seems to want to be descended from:
William had a very brief tenure as Chancellor - at most 3 years (and they happened to be plague times!).
What I have read is that he died with no male heirs! (That fixed 'em!)
His heiress is supposed to have married a Mure who inherited the Caldwell property on the Ayrshire/Renfrew border. End of the direct Caldwell connection.
Straiton is way down south in Southern Ayrshire and a whole different ball-game - there was about 300 years and probably 12 generations to filter down to get to William of Straiton. Straiton is up a valley and probably not a wealthy property area in general so William of Straiton was possibly no more than a tenant farmer or even a tradesman.
I think it is a very long bow to try and suggest that WofS is descended from The Chancellor.
We have to know and believe that the Caldwell's were pretty thick on the ground pre-1600's. I am starting to think it might mean "Smith".