You'll be fine on I-40 and I-81, unless another major weather system comes through. The interstates are almost always passable, except right in the middle of blizzards like I described above. But those are very rare here.
But like others have said, that's not the most pleasant drive. 40 is mostly flat and boring, and 81 is usually full of tractor-trailer traffic.
The problem is that there's really no alternate routes unless you're willing to really increase the trip time and mileage.
Good luck and have fun.