You could order his death certificate. If he died of complications relating to his condition, it will be listed as the cause of death or supporting cause of death. Sometimes medical conditions unrelated to the death will be listed as well. His exact death date will be included and by 1952, I would imagine his exact birth date would be as well (earlier death records often only listed the age at death).http://www.health.ny.gov/vital_records/genealogy.htm
It looks like uncertified copies of death certificates in New York are available to the public 50 years after they were issued so since your uncle died in 1952, you shouldn't have any problems ordering it.