Is it possible to select a surface with the Fillet Feature and then deselect some of the edges of said surface? 

I'm trying to apply blends to some edges of a dynamic part.  The problem is that one of the surface's placement is driven by the width of the part which is subject to change, and when it moves it comes into contact with multiple different faces, creating entirely different edges.  This causes any blend put on one of those edges to fail.  The obvious answer would be to just select the face, but that face contains edges that must remain sharp.  (Keep in mind that the edges that cannot have any blend applied to them do not change)

I tried using the "Multiple radius fillet," but when I set the edges to 0, I get a Rebuild Error "Loops or faces with common edge(s) cannot be assigned multiple radii."

My only option is is to create 6 separate blends with 6 respective configurations for the 6 different surfaces along it's path.  This is not a favorable solution considering that other people will need to use this file.

The idea of deselecting edges of faces seems simple enough to me, I just cannot figure out how to do it.