Given his age, profession and family needs, there are good reasons for no military service file to be found in his name. Physicians were exempt from military service because home communities, free and slave, needed the services of these men. Those who entered the military did so on a voluntary basis. Since Dr. Fergeson wasn't a young man and had a family, he would have been inclined to remain at home and tend to the needs of people in Lebanon VA.
As for your question concerning the Confederate cross, a local Daughters of the Confederacy chapter probably decided to place this marker based on testimony about his care for sick and wounded soldiers. Of course he may have done all this without ever putting on a uniform or leaving Russell County.
People tend to forget that doctors were needed at home as well as in the army.