Frank, the handrails were fairly easy to remove. They are just screwed down with large flat head #3 Philips SS sheet metal srews through the handrail into the cabin top. There is nothing holding the rail from inside the cabin, thank God. I used a couple of 1.5" putty knives and a large flat blade screwdriver at each attachment point to work the caulk and free the rail. There are 5 attachment points on each side with a total of 9 screws on each side. The bungs came out easily using a very small screwdriver and digging the bung out starting in the middle of the bung. Care must be taken not to mess up the edge of the hole.
I believe I'm the first owner of this boat to remove the rails. It looks like they had been refinished in place in the past. I'm a firm believer that the proper way to refinish exterior teak is to remove it, sand it down, refinish and then re-install. I tried a half hearted attempt at refinishing one handrail while it was on the boat last year but was not satisfied with the results.
The question of reinstalling the bungs came up because the old ones really did come out cleanly and fairly easily. It just got me thinking that maybe the original ones were not glued in at all. I'm going to try the dipping in varnish method that Ted described for the reinstallation process. I may even soak them in varnish for a little while since they appear to be just a tiny bit small for the holes.
Thanks for the feedback team!!!