"The article I wanted to highlight was two brothers, former confederate soldiers who were banned from owning firearms. These brother known as the Thompsons. They built themselves bows and hunted a variety of different game......"
First, the article you reference is "highly" inaccurate as to the information concerning the Thompson brothers. I would suggest you ignore it and do as Blackhawk recommends and read "The Witchery of Archery" by Maurice Thompson. Get a reprint of the 1878 or 1879 editions first. These are the two editions that Maurice compiled and published. Then read the 1928 Edition edited and published by Elmer. This one has the article on hunting in the Okefinokee Swamp that Will Thompson published in 1915, 14 years after the death of Maurice. Maurice did not publish anything on hunting in the Okefinokee Swamp until sometime later, and that was not on the trip he and Will took after the Civil War.
To give you my thoughts on your question. If one followed the Thompson's leads on being banned from using firearms as former Confederate soldiers, one would ignore it and continue to use firearms. That is what the Thompsons' did.
A common misconception of the brothers is that they used bows because they were denied their use due to their Confederate status, but actually they were using bows prior to the Civil War and continued to use them[along with firearms] after, because they preferred and enjoyed using bows.
It is all there in "The Witchery of Archery," pistol, rifle and shotgun.
The Witchery of Archery – 1878 [pg. 36, 38, 110, 111, 123]
" … Snuffing a smell of fun in the air, I sprang into my rubber boots, buckled on my quiver an pistol, strung my bow, and , in much less time than it takes to write it, was plashing through the water in the direction of the dog, which was now baying loudly, evidently keeping at a respectful distance from his enemy."
" … At this moment Will reached the ground, and lodged an arrow in the cat’s flank, while it was so close to me that I shot it twice with my pistol, being unable to use my bow."
"… I killed a deer with my rifle, just before night-fall, the only one we saw while on the river, and we were glad to add its venison to our supply of provisions."
" … On one of these latter Will used my shot-gun to good effect, but the birds, on being dressed, gave forth a decidedly fishy odor, and we threw them away."
"… So, some years later, I returned, and all alone, in a mere shell of a skiff, very narrow and shallow, and armed with nothing but a small Smith & Wesson pistol and an English long-bow and arrows, explored the lake in every direction."