First, having been born in 1818 Henry would have been 42/43 in 1861 and well above the age of conscription, so he would not have been "drafted" to serve in either army.

Certainly this does not mean that he did not serve for men far older did serve in both armies. However, as much as we hear of these stories of old men serving it seems to have been rare, because Army life on either side was tough, especially in the Infantry. Mid 40's is not that old today but after a hard life of working in the fields in the early 1800's, the mid 40's was like a man in his mid 60's today.

Older men tended to serve in Artillery or Cavalry, or were occupied as Teamsters or Blacksmiths where they could ride rather than walk. That might be some key points that you might consider in your search.

Second check the other men in the regiments with your Henry. Where there other family members in that regiment? Cousins, nephew and uncles, fathers and sons, brothers tended to join together. was the company that Henry was a member of recruited in his home area? This usually applies to the Confederates. But would not apply to the southerners in Union service.

Outside of that, without finding a record such as a prisoner of war record, an Oath of allegience, a pension (probably too old to have lived long enough to recieve a pension) or some other record which would have recorded his age, you may not be able to make a definate determination as to which of the three Henrys that you have already found is yours, if any of them are.