Not sure how relevant some of this other information is but yes, likely a water snake so no worries. In the unlikely event that it was a copperhead and did actually bite you, it wouldn't amount to much more than a spoiled afternoon of fishing. Painful as it may be, with proper care you would be fine. Timber rattlers on the other hand are another story... Only other snake you will likely see is the northern black racer, which I see the most. A harmless snake but can become very aggressive and will bite if not left alone. Remember that all snakes at least in the GSMNP are to be left alone and certainly not killed...
Regarding the venomous pit vipers that reside within the Smokies, it takes a lot of energy for a snake to produce and store venom. They need it to survive and will in fact ration it out at times. They can tell that we are not food and will often bite without injecting any venom at all. This is referred to as a dry bite and is often a defensive move for the snake. Along those same lines, it is also thought that younger, less mature snakes have not learned how to ration their venom yet with a bite often emptying their entire venom reserves. Something to remember when you think that the small baby copperhead you come across might be somehow less dangerous.