Enjoy your trip down here to Tennessee !!!
The previous replies have pretty much captured it as to TN law. There is no requirement placed on you to notify; however, if you are stopped by LEO and they ask you if you have a weapon, and you are a CHL holder, you do THEN have to advise them IF you are armed.
Anywhere outside of the metro areas, they are pretty laid back about CHL and OC. Lots of places in Nashville are posted, but not all, by any means.
If you're coming to Nashville - just stay off the interstates anywhere around rush hour !!!