For this example I'm using a polyCube with 3 inputs. SkinCluster1, blendShape1, and tweak1.
Let's say I want to delete JUST the blendshape node.
If I use the delete history tool, it'll remove all of them.
What I can do is directly select the blendShape node and delete, just as you can do with almost anything in Maya such as a nurbs or poly surface.
What I do to select this node, is simply highlight and copy
And then paste into Maya's search by name feature. NOTE: if you don't see this feature, you may have to
hit the drop down menu circled in RED and pick "Search by Name"
Now you should see that you have your history's input node selected
Now from there you can just hit the delete button. And you're done. Here's what it looks like on my polycube with just the blendshape gone.