There isn't any real halakhic requirement to kasher items that are any degrees of separation from food. You only need to kasher items that are directly being used to cook food.
The only time we are required to apply the Koshering Process is on items that are normally used directly on the fire, or are in contact with hot foods that are directly on the fire. These are called Keli Rishon and Iruy Keli Rishon respectively.
Sinks, refrigerators, trash cans, counters, dishwashers, stovetops, tables, cutting boards, mixmasters, silver kiddush cups, and anything not used with hot foods from the fire do not need any koshering.
Silverware are typically kashered because on occasion one uses them in the cooking process, therefore it's easier to kasher them along with anything else. But nothing else "needs" to be kashered, or even covered since:
1) it's not being used in the cooking process
2) the temperature of its involvement is diminished to the point it can't absorb, or it can't transfer what it has absorbed back into any of your vessels
So there aren't any degrees of separation to worry about, one only needs to kasher the item directly involved with cooking food.