I'm always cautious about giving pruning advice without physically seeing the tree(s). With that said, I will provide you with some general guidance and suggestions. My first thought with regard to your question is whether or not it is even necessary to "remove" the double stem--is this tree causing problems or is it a hazard/liability concern? Do you wish to remove this "double" strictly for aesthetic or cosmetic reasons?
You're not likely going to kill the residual main stem by pruning out a "double" from it and I would advise against painting the stump wound as it is unnecessary. This, of course, is based on the assumption that you absolutely want/need to remove this double stem. I'm a staunch advocate of dormant season pruning--always have been and I always will be.
In addition, I would strongly encourage you to contact a certified arbortist if this pruning job is beyond your chainsaw capabilities. Pushing your chainsaw operating skills by cutting out this double stem is certainly not worth it.
For a more thorough answer and a legitimate on-site assessment, please contact a local forester in your area.
Best of luck!