YES, you can decide which edges to show in 2 ways.

Method 1. by hidden edge selection

  1. select the edges you want to see
  2. invert the selection
  3. run the hide selection command
  4. render

any edges that are hidden on the base selection of the polygon object are also hidden in the shader.
This works only for real edges A-B B-C C-D D-A

Method 2. Create a weight map.
  1. Insert your weight map as the size Driver in the modify Tab.
  2. render

edges will be smaller where weight is less.