The word ‘tawse’ for ‘a split leather strap designed for the chastisement of children ‘ does appear in the Oxford dictionary, the standard reference for UK English. The book you refer to was published in the early /mid 19th century as far as I can see, and at that time there were significant dialect differences between regions of England , let alone Scotland.
I think US standard and many spellcheckers, although i stand to be corrected, are more normally Harper Collins which I would not expect to carry the word.My spell checker certainly doesn’t.