You do not have to be a descendant to order a government marker for a Union or Confederate vet. I have personally ordered over 20 (at least 17 Union and 3 Confedeate) for vets buried here in Payne County OK. Each time I write in the blank for person ordering the stone that I am graves registration officer for the local SUVCW camp.

As long as the cemetery official signs off on the order form, you shouldn't have a problem.