I've already been down these roads.
Take a copy of the no tag displayed statute with you. Show it to the LEO that stops you. They will be polite (in my experience) and let you go.
As for the CDL, I got mine. My reasoning was if something happens and there's an accident (I have a military tractor-trailer registered as historic), I may be charged with operating a vehicle without the proper license and it would be my fault. Yes, you might get off after a court (expensive) battle. But the lawyer will charge more than it costs to get the CDL. Just one less thing to worry about. And, if you take a class with on the road training, you will learn how to safely operate a large, heavy vehicle.