For a custom ICC I think I would need a colorimeter, is there some cheap options? I'd love to print it by myself but I'm not sure I want to invest in a colorimeter for such small printer
You can either have a service make a custom ICC profile for each paper on which you want to print B&W, or you can use a spectrophotometer to me them youself, which you may be able to rent.
When the service makes you a custom ICC profile, if prices are similar to the U.S., there would be good services starting at about €25 for each paper. You download a profiling target, use Adobe Color Printer Utility to print it on the paper you want profiled, mail the printed target to the service, and they e-mail you the ICC profile. Some services will build custom ICC profiles specially designed for neutral B&W.
To do it yourself, the device you use is a spectrophotometer, not a colorimeter. In the U.S. I rented an X-Rite i1 Studio spectrophotometer. It cost me about $75 (€66) total, and I had it for a week. In that time I made 12 or 13 custom profiles for different papers. The X-Rite software is easy to use. The profile quality is good enough for me. Now I get neutral B&W prints on several papers.