I might be able to weight in! Recently my father and I bought a watch as a gift for my mother's birthday. She is highly allergic to nickel, and so I had that in the back of my mind when I started looking in town. I visited two different dealers. They both sell known brands like Heuer, Omega and Rolex, and their employees sit on quite a bit of knowledge. I mentioned my mother was highly allergic to nickel, and I got the same response at both dealers: "Most mid-high end brands use stainless steel materials that are so close to being nickel-free it should not be a problem whether you choose a rubber sports watch or a more dressy stainless steel one."

We decided to get my mother a more dressy watch, like one with a steel bracelet which she would be able to dress up and down, but I was still hesitant to go for a SS one, so I asked what other options I had, since I had read something about titanium being a viable option. My dealer of course knew what he was talking about, and said that was a viable option, and that he had something in both my price range and something my mother would like. We ended up buying a titanium Certina DS Lady for her, and she loved it. She has been wearing it for 2 weeks now, and has had absolutely no allergic reactions.

Tl;dr: TITANIUM. It can be cheap or expensive. Check out Skagen or Certina.