I think you will need to do this in two parts.
1) Create a plot with all "node degree > D" and set its edge color to None
2)Create a plot with all "node degree < D" and set its edge color to what ever you want
Using "hold" to combine the two plots.
The issue will be that you will need to first do the Delaunay triangulation then sort out what data needs to go in what plot (ie you will need to use some of the same nodes in each plot, you cant simply treat it as two separate triangulations).
Let us know how you get on.