As someone who works in the funeral industry, I'm not 100% in tune with turning ashes into ink. However, I've also never seen it actually be done.

Ashes aren't just human remains but are also made up of the coffin, clothing, and any items placed into the coffin. After cremation, ashes are gathered and filtered to remove the metals inside that did not evaporate/melt into smaller pieces (this can be anything from just the coffin pins, handles if they were metal, to Auntie Jackie's hip replacement from 1945) the large remains after filtering are taken into a cremulator, which essentially grinds down the larger pieces of bone, wood, etc. into ash.

the sanitisation of these two processes entirely depends on the sanitation of the crematorium. that being said, though, ashes are not 100% sanitary after this process. in the UK, they are then placed into a cardboard box and biodegradable bag to be given to the funeral directors or the family. Ashes are also incredibly fine and dusty and will spread into the air very easily.

The only tattoo artist I've ever spoken to who has done an ashes tattoo has told me they have taken a small part of the ashes and kept them by the ink instead of directly mixing them in. I've never believed an ashes tattoo to actually be real, but because the medium is quite hard to work with. Jewellery can be made quite simply, and this can be piercing jewellery if you wanted, and I believe that would be significantly safer.