There are a number of "eco-friendly" pens and pencils on the market advertising recycled content and other "green" features, but are they really as good as they look? Many standard wooden pencils use wood from fairly well-managed sources, and "green" pens still seem to use fairly standard disposable ink cartridges. So is there really enough of a difference to justify the advertising and premium prices?
I would be surprised if any pen would be more sustainable than a sustainably sourced pencil.
In terms of sustainability, I still think that "green" pens should come after refillable pens, pencils and fountain pens.
There are also refillable cartridges for standard fountain pens, which usually come with plastic cartridges. For example, this middle one looks (and is) a plastic cartridge for a fountain pen, but the red end twists and is able to suck in ink from an inkwell.
At one point I used such a model for many years, which should be more sustainable than any other type of pen (feathers aside, I guess). Now I use almost exclusively mechanical pencils (and chalk on a blackboard).
So my verdict for your green pens:
"Green"? Maybe more so than others. Sustainable? Not really.