You can request a lookup from social security, usually the catch is if you can't prove someone has died, but you do have his death certificate. It costs around 29.00 and they won't refund it if they don't find it. It also depends if he was working age when social security came into being, the early 1930's.
I just looked at his death certificate online. It says he was 84, so it is very doubtful he applied for social security.
I will keep looking around and see what I can find. What was his wife's name?