Not too familiar with this particular Year/Model, but for 1960's Chevys in general;
Look for a set screw, like a (very) little Allen wrench headed bolt with no head, or maybe a small slotted screw with no head, around the back of the knob, that screws into the knob and against the shaft. Loosen the set screw, and the knob should come off the shaft.
The part that holds the switch in the dash is called a bezel, and there are special sockets you can get to remove them. If you can find one that fits, just put the fingers in the slots of the bezel (after the knob is off), and turn counter-clockwise to unscrew the bezel, and the switch will come out through the hole it's mounted to in the dash.
You might have a hard time finding one though, and they're not cheap because not too many people make them. Check with Snap-On, MAC, Matco, or look in your local phone book under tools or tool dealers. Or maybe do a Google search for bezel socket?
If you can find a helper or 2, oftentimes you can set a flat-bladed screwdriver against the side of each the slots in the direction you want to go, on both (or often all 3) of the slots, and tap them simultaneously. If you can't find the correct tool, it might be your only chance.
Oh, one other thing you could try. Find a socket that is the right diameter, and use a bench grinder or Dremel tool, to grind away the shell of the socket opening, leaving some fingers to reach into the bezel slots. If you use a 12-point socket, grind away 3 points out of every 4, so the will be evenly spaced, then whittle down the remaining 3 points until they fit in the slots.
