http://archive.tennessean.com/assets/pdf/DN17011528.PDF
This precedes the Right to Hunt and Fish Bill-
The TN Attorney General has issued an opinion that TWRA has the ability to regulate hunting in TN, and as long as firearms are discharged for the purposes of hunting, it is legal. This is an Attorney General's opinion, and NOT TCA. I would run this by the local PD(and someone high up enough to make the call) and get it in writing from them- court costs are still court costs. They may not be aware of the Right to Hunt and Fish Amendment and how it pertains to hunters on their jurisdiction.
This also does not protect you from reckless discharge charges. Know where your round will land.
Personally, I would prefer to firearm hunt