Getting the entry of birth is the only sure fire way.
You could try eliminating the impossible (the Sherlock Holmes approach). In 1861 Isabella appears as niece with William and Charlotte Coxon. This implies Charlotte was aunt and Sawyer. In 1841 at Sneyd Green, Burslem: James, Elizabeth, children Charlotte, Isabella, Joseph, David & Mary. 1851 same location with younger son James 10 and granddaughter Eliza 6.
It appears Isabella married Robert Stewart 1848. Appears Joseph died 1840.
David baptised Wesleyan Burslem 11 Aug 1834 James Sawyer, Elizabeth Oakes (see IGI and the other place). Recorded with family 1841 & 1851, but no trace afterwards. (Note: IGI baptisms for David 1834 gives Elizabeth Oakes, Charlotte 1824 just Elizabeth and Isabella 1826 Elizabeth Burchnall, yet the 1841 census indicates they were siblings.)
Mary b. 1838 appears died 1854. Very young, but possible illegit birth. James really was too young.
Mary looks the most likely, but it's far from solid. Maybe someone out there has access to baptisms, though if illegit Isabella may not have been baptised.
Good hunting, Dion