You could use KOR, but the country we were defending was the Republic of Korea, ROK. You could also use RVN for Republic of Vietnam.
I have seen "KOR" and "VN" on headstones and such, but I don't know if that is a funerary custom, or just a pragmatic thing. They aren't the proper names politically, but I realize that's not the point, although I think it is more consistent also with what our troops used to call theirs: ROKs ("rocks") and ARVNs ("Arvins").
ETA: "1942-66: WWII, ROK, RVN" is 23 characters with spaces.
ETA2: Arlington undoubtedly has written standards about every conceivable thing, but since this is a brick and not a national cemetery, maybe it's not worth the worry.