Hi Kate,
I have looked on the IGI & found some baptisms although they may not be the correct ones as Ann/Hannah is not mentioned.
THOMAS AUSTWICK
Christening: 27 AUG 1820 Snaith, Yorkshire, England
Parents: Father: JOSEPH AUSTWICK
Mother: ANN SHEPHERD
RICHARD AUSTWICK
Christening: 03 JUL 1823 Snaith, Yorkshire, England
Parents: Father: JOSEPH AUSTWICK
Mother: ANN SHEPHERD
MARY AUSTWICK
Christening: 12 MAR 1826 Brayton, Yorkshire, England
Parents: Father: JOSEPH AUSTWICK Family
Mother: ANN
SARAH AUSTWICK
Christening: 13 APR 1828 Brayton, Yorkshire, England
Parents: Father: JOSEPH AUSTWICK
Mother: ANN
JOHN AUSTWICK
Christening: 30 JAN 1830 Brayton, Yorkshire, England
Parents: Father: JOSEPH AUSTWICK
Mother: ANN
WILLIAM AUSTWICK
Christening: 30 JAN 1830 Brayton, Yorkshire, England
Parents: Father: JOSEPH AUSTWICK
Mother: ANN
MARTIN AUSTWICK
Christening: 27 NOV 1832 Brayton, Yorkshire, England
Parents: Father: JOSEPH AUSTWICK
Mother: ANN
RICHARD AUSTWICK
Christening: 21 JAN 1835 Brayton, Yorkshire, England
Parents: Father: JOSEPH AUSTWICK
Mother: ANN
If it is the correct family, at least you know the mother was Ann Shepherd & there was a birth for a Hannah Shepherd at Sherburn in Elmet 20th October 1791.
Gill