Here's some Cady's from a few southern Steuben county cemeteries.
Perhaps you can research the oldest Cady's among them and find some leads. I did not see Elizabeth Cady Cook. Happy Hunting!
CADY Cem. Lindley, Steuben, NY
CADY, John, Died 23 Aug 1850, age 76y1m19d
CADY, Permelia Frink, Spouse of John, Died 3 Feb 1862 , age 85y2m3d
CADY, Samuel, Died 27 May 1875 , age 74y3m13d
CARD Cem. Troupsburg, Steuben, NY
CADY, Aurilla * Spouse of Hollis Burr, Born 13 Feb 1798, Died Oct 29, 1850 d/o Matthew & Dorcus Richmond Grinolds
CADY, Burr H*, Born 1838 , Died Aug 9, 1847 Son of Hollis & Aurilla Gringolds CADY
CADY, Clarinda L.* , Born 2 Jun 1824 , Died Mar 18, 1845 Dau of Hollis & Aurilla Grinolds CADY
CADY, Clarinda Sabrina*, Born 3 May 1845 , Died Aug 6, 1852 Dau of Levi & Olive Card CADY
CADY, Fanny*, Born 1863 , Died Oct 1863 Children of LR & MA CADY
CADY, Hollis Burr* , Spouse of Aurilla Grinold , Born 23 Dec 1795 , Died 3 Apr 1858 s/o Jonathan & Miriam Chaffin
CADY, Joseph A* , Born 1860 , Died Sept 28, 1862 Children of L R & MA CADY
CADY, Olive* , Spouse of Levi Randall , Born 17 Nov 1827, Died June 17, 1859 d/o Rev. Charles Card & Phebe Gardner
CADY, Sabrina*, Born 14 Dec 1840 , Died June 15, 1842 , Age 1y 6m d/o Hollis Burr & Aurilla Grinolds
Mount Hope Cem, Troupsburg
CADY, Blanch, Spouse of Forrest, Born 1919 , Died 1944
CADY, Burr Hollis , Spouse of Lucy Davis , Born 1849 , Died 1919 s/o William Reed & Mary Elizabeth Rogers Cady
CADY, Carlin, Born 1943, Died 1944 Child of Forrest & Blanch Cady
CADY, Charles C, Spouse of Metta J, Born 1869, Died 1944
Potter St Cem., Troupsburg
CADY,Erastus,Born Oct 14 1899,Died May 15 1900 Son of EJ Cady
CADY, Eva H. , Born May 12 1867 , Died June 15 1899 Dau of William Reed & Mary E. Rogers Cady
CADY, Irey, Died Apr 15 1880 , Age 5 weeks
CADY, Levi Randall, Spouse of Olive Card, Mary Abigail Davis , Born May 21 1821 , Died May 25 1888 s/o Hollis Burr & Aurilla Grinolds Cady
CADY, Mary , Spouse of Levi R. , Born Feb 11 1838 , Died Apr 23 1902 d/o Joseph Whipple Greene Davis & Fannie Phoebe Chase
CADY, Mary Elizabeth, Spouse of William Reed , Born May 13 1830 , Died 1923 nee Rogers
CADY, Nancy, Spouse of Ranson, Died Mar2 1858, Age 55y 7d
CADY, or NUDD Darwin, Died 1922 could be Cady/ Nudd
CADY, or NUDD June, Died 1925 could be Cady/ Nudd
CADY, Ransom, Born Jn 15 1839 , Died Jn15 1839
CADY, Ranson , Spouse of Nancy , Died Feb 12 1884 , Age 85y 11m28d
CADY, William I, Died Sept 15 1869 , Age 3y 9m 18d Son Of William & Charlotte P
CADY, Willian Reed, Spouse of Mary Elizabeth Rogers , Born Dec 21 1822 , Died Apr 5 1897 s/o Hollis Burr & Aurilla Grinolds Cady
Griggs District Cem., Troupsburg
CADY, Sybil,Spouse of Jabez Cady,Died July 15 1828,Age 21y 8m8d
CADY, David Michael, Born Apr 1 1990 , Died Oct 1 2007 s/o Michael L. Cady & Lynn A. Covell
CADY, Donald, Born 1940 Died 1940Son of Forrest&Blanch Cady
CADY, Duglas,Born 1942 Died 1944 Son of Forrest&Blanch Cady
CADY, Forrest, Spouse of Blanch, Born 1919 , Died 1944
CADY, George, Spouse of Mary, Born 1878, Died 1964
CADY, Harold, Spouse of Jessie, Born 1919, Died uncut
CADY, Harold B, Spouse of Loretta M, Born Jan 11 1920 , Died May 11 1991
CADY, Jessie, Spouse of Harold, Born 1919 , Died 1944
CADY, Jimmy,Born1937,Died 1937 Son of Forrest & Blanch Cady
CADY, Kate, Spouse of Ray, Born 1885, Died 1970
CADY, Loretta M,Spouse of Harold B,Born Mar 1 1926, Died uncut
CADY, Mary, Spouse of George , Born 1884 , Died 1918
CADY, Metta J, Spouse of Charles C, Born 1872, Died 1932
CADY, Ray, Spouse of Kate , Born 1885 , Died 1973
CADY, Robert, Born 1938 , Died 1944
CADY, Thersa, Born 1942 , Died 1944