Also, when I attempt to order my grandfather's records in preparation for his funeral, what if I find out it has not quite been 62 years and they are not held as public with the National Archives?
You may be able to have his next of kin place the order or you may still be able to request limited information from their Military Personnel File.
How would his next of kin be able to order the records?
There are several options for the next of kin to be able to do that, but the first way would be to mail or fax a Request Pertaining to Military Records Standard Form SF 180 to the National Personnel Records Center.