No shoulders is pretty common for low-traffic routes, particularly in the mountains.
Unfortunately, google maps won't show you the traffic density for a road. It's not a big deal when you're dealing with 5 cars passing you each hour, except Mr. Murphy will insist three cars will pass you at the same time as the other two are coming towards you.
Check out "vehicular cycling" for some tips on how to handle this situation. Basically, remember you aren't impeding traffic, you ARE traffic in South Carolina, North Carolina, Tennessee, Virginia, and Kentucky. (And the rest of the states.) Take the lane when there's not room for you and a car passing you in the same lane, or when they can't pass you safely because of a blind curve or hill, and help them pass you when it's safe.
Particularly for your intended route, I'd advise you to deal with it. If you insist on roads with shoulders, you're going to be dealing with high speed, high volume traffic, which is no more safe than winding, low traffic roads, and is probably more dangerous.