Hello. Then I would say he was buried at Helena because he died with the smallpox.
The health officials had no other options at the time as it was so easy to catch. Where you died was where you were buried meaning if you died in a certain area, that was where you were going to be buried. He could have been moved to Memphis after the war as I think that is where some of the Union dead were taken. All in all, the Union dead were better taken care of is my belief. What does his service record say? Have you checked the area around Helena or Memphis?
My ggg grandfather, a CSA POW died with smallpox in the Federal Prison in Little Rock with smallpox on Feb. 1, 1865. The family was not allowed to claim his body because of this disease which people feared so greatly.
We believe my ancestor was buried at Mt. Holly and then moved after the war ended to just outside the National Cemetery.
Someone like Bryan Howerton might have an idea.
It has been my experience that if you can find the group Childs was taking care of, it might be written up in a state site with stories of those units speaking of the illness and who died with what.
Just because you have not found it, does not mean it is not out there somewhere, so keep on looking would be my advice.
Good luck with your search.
Linda