Hi Annelot
Many water-based ink formulas employ ammonia as an anti-fungal agent, but it's also worth investigating sensitivity to hardeners,
which often are more readily reactive and can cause "allergies" also, but vary more so in differing ink formulations.
Considering the health related import of your question, I'm going to recommend that you contact a chemist at Visprox (Netherlands) regarding their offering:
and raise the issues to that expert that you've raised here.
Note that if you find few options exist, enabling a heat-curing ability would allow you to consider inks (modern EF plastisols) that have few, if any, reactive chemicals present in their formulas compared to many of the "water-based" types.
Happy trails!