The SSDI was pulled from the site I used to send people to, so I went looking. This looks like it should work for you.
You want #1, -- Photocopy of Original Application for Social Security Card (SS-5) -- Line A, enter $27.00.
From the index I sent you the Soc Sec number is given, so the fee you need to pay will be $27.00.
Don't worry if you do not have all the information requested for the deceased. You have the SS number and that should suffice. With that number they can see from their own records the person is deceased etc.