Keith,
I buy plants from Bob Smoley and most are cuttings. He tells me to set on top of pure perlite and don't water it until you see growth. I would put that on top of perlite and just mist with water with a table spoon of peroxide in it. I would mist only once a week and not wet the cactus at all. You may not see growth for a year. I would also not cut out the rot. I know of this happening and I didn't and mine healed itself leaving a brown scar. That cactus is now 3 years old and looks great.
I have seen some on Ebay and they are not cheap. It's aways the variegated ones that are the hardest to grow.
Stush
