Denture cleaner tabs are also effective as is a small amount of washing powder or dishwasher powder - just make sure the decanter is well washed afterwards. We don't drink whisky so didn't know that the decanter full of expensive whisky tasted soapy!
Instead of crushed eggshell, you can also use drawing pins or baking beans. The key is to use something hard and abrasive that will scour off the staining.
get a dish cloth or something, and drape it over the end of a long thin piece of wood, such as a wooden spoon handle, and then use it to scrub the sides of the decanter. just don't get the cloth stuck!