If you have a motorized Z, you can out focus Z roughly 10 to 20mm on a vector line increasing its width substantially. With the correct speed and power (cardboard or paper is going to be really fast speed and low power) you can remove a small amount of material without cutting though. All this requires is experimentation, your time, your machine, and your materials.
Here is an example of out-focused Z at various distances:
Also, I just so this posted: