No evidence for maiden surname of Shaw.
Christening date claimed does not apply to this Martha.
Martha Shaw, christened Halifax 6 January 1632/33 was a daughter of Abraham-1 & Bridget (Best) Shaw of Dedham, Massachusetts and their daughter Martha married only Thomas Vinson.
Russell Franklin Shaw, "English Ancestry of Abraham Shaw of Dedham, Massachusetts", The Genealogist, (10 [Spring 1989]: 86-97.
https://www.americanancestors.org/DB2817/i/62887/86/10006609389