These are some of the options to try to get his records.Provide each with as much information as you can about his military time that you can.Best I can do you.Would love to know the outcome if you find the time.
VA - Regional Office where he last lived.If they don't have any info, I think they pass it on to where he enlisted/discharged.Be sure to mention FOIA in your letter and in the address.FOIA is Freedom of Information Act.
Contact the County Clerk of where he might have enlisted and or been discharged and also try the State Archives of the state he lived in and where you think he enlisted/discharged.
If he had a military funeral, contact the Sexton of the Cemetery and also the funeral home.I believe they have to have records of some sort that prove he was a veteran.
Even though you don't want his full records, I would still try the NPRC in St. Louis.If they tell you they burned, resubmit using the additional paper work they send you. Give them some time then call them in about 4-6 months and keep track of when you make contact each time and who you speak to.Sometimes they are able to recoup partial records.A retired LTC told me that the NPRC doesn't seem to interested in helping people trying to recoup WWII records.
Was he a member of any VFW chapter?If so, check with them.
Here's a link giving info as to recovering records.
You can also write to the Department of Military Affairs in the State where your relative lived or served.
You can order copies of Veteran Records by writing to: National Archives Records Administration, General Reference Branch (NNRG-P), 7th & Pennsylvania Ave NW, Washington, D,C, 20408 or call (202) 501-5170 to ask for order forms and prices