I'm not on the research team, but I go to Binghamton and have tattoos and a shitty immune system! What I did was got a teeny tiny dot to try it out on the side of my foot with whatever ink that the tattoo parlor in my city uses. I forgot the name of it, but I did look it up and got frustrated and said fuck it and monitored my symptoms. I was just fine! It caused my entire foot to be very itchy for 2 days but it didn't swell and it wasn't extremely itchy. I went back the next week and got about a 3-inch tattoo which healed fine (granted, I was diligent about aftercare, monitoring my symptoms, taking my meds, taking vitamins, etc). Also itchy but not crazy. Also, the dot on my foot faded within 3 months because that part of your skin can get sweaty in shoes and rub against socks and other materials.

I would definitely consult with the tattoo artists at the parlor and ask what ink specifically they use and do some research. Then, try it out on a small patch of your skin to see how you react.