Not much left to say
Jim gave a pretty good illustration of how to do this.
You simply divide your suppliers into groups (like your C class), and decide what kind of evaluation you think is appropriate to each group.
Then you write it down in your procedure, and you do it.
As long as you do this, you are following the rules.
As an example, in my company we have many items for which there is only one supplier we can use. What kind of criteria do we use for choosing to make a purchase from them? The fact that they are the only ones who can make it for us!!
What kind of evaluation do we submit them to? Not much. The only thing that needs tracking is their dependability so that we can lodge complaints with them if it gets bad. But there's no way we can pull the business from them.