If you are referring to a VA Confederate Tomb Stone, requirements, to my knowledge do not, require a living relative's signature. Only proof of his service such as may be procured through the service noted in the red enclosed box above. The UDC can be quite hidebound.
I've been able to obtain a number of stones for non relatives.
You can do the paper work yourself, see: http://www.cem.va.gov/hm_hm.asp
The nearest Sons of Confederate Veterans Camp, SCV, will in most cases help.
And, the Cemetery management will usually have the VA forms and will assist, and in some cases, take care of the whole business provided you offer proof of service. However, they might charge to set the stone. Again, the SCV members will usually perform this along with a memorial service.
Good luck,
George Martin