Chris, I would do a little more digging in Census data to get some potentials. I didn't see anything that looked good 1865 NY State census but do look at that further.
For 1850 US Census a couple things I noted: John Cornell, 10 years old, of Stephen and Mary Cornell in Ossining, Westchester, NY; and a John Cornell, 10 years old, living with a Caleb and Levina Purdy in Harrison, Westchester (appears to be an orphan). A few other potentials in the immediate NY area and then some farther away such as Chemung County, NY. Also look at southwestern Connecticut and Queens or Kings Counties in NY.
By the way, his Illinois death index record gives his year of birth as 1840 rather than 1839 but that is info reported at the time of death.