I have used Diamondback radials on several cars. They are the best tires I've ever had on my Cadillac. The ride and handling is far superior to that of bias ply tires. They are immensely superior to the horrible Coker radials I once had on it. Coker doesn't have a very good reputation in the classic car community.
Even Corky Coker told the president of our Cadillac club that he would use Diamondbacks if he intended to drive the car rather than just show it.
They should work fine on your original wheels. I have them on my '39 Packard which uses 4.5" x 16" rims. They're expensive but if you want wide white walls, they are about the only way to go.
Your rims shouldn't need an inner tube. My Packard doesn't use tubes.