I certainly don't have deep knowledge in this area but my understanding is that the cartridge is basically a cavity with a small hole at the bottom and a piezo electric element at the top to sputter liquid down. The tolerances are tight but considering how advanced manufacturing is, I would imagine someone competent could design and prototype it with the tools and manufacturing ecosystem that's available now.
There's at least one project that has tried to design an actual DIY/open-source inkjet printer [0], along with inkjet print heads [1].
The ink most likely need some special sauce? But I imagine there's many organizations that can specialize in making the ink so that it can be treated close to a commodity. If not, maybe this can also be engineered?