When i make a country ham, I soak it for 2 - 3 days to get the saltiness out. Changing the water frequently. It should work as well for a CB. Add more spices when you change the water. I always add more to the cooking liquid.
As everyone has already said, soak and rinse, soak and rinse, then boil and rinse even more. If all else fails, use very small chunks of it in large amounts of starchy (i.e., beans or lentils) soup. It will still be yummy.
And yes, I bought a Virginia country ham one year and you literally (even according to the instructions on the bag) had to soak it in the bathtub for days on end. Even then it was pucker-your-mouth salty. My parents were visiting, and they said it reminded them of the hams when they were kids.