Handling "contraband" tattoos in closed-book exams
"Cover it up" seems the only realistic solution if it appears to be a tattoo.

However, since we're discussing this in the hypothetical, writing a theorem on your arm may serve as a nice reminder of a basis from which to work on problems, but it can't really answer something useful for you. Just as younger students tend to look at their fingers when counting, they still have to put in the work of translating an abstract numerical problem to their fingers, then "read" the information from their hand, and finally write their answer down. We don't restrict their fingers as counting tools. Advanced students make more elaborate associations between concepts they're learning and something concrete -- this is usually encouraged by instructors when we explain things in plain language or metaphors. So, your question makes me think about what questions I'm asking my students. If it's just "Write down this definition from memory", then maybe I'm not going deep enough in the topic. Suppose instead that I said something like "Here's a definition of a key term you can look up anywhere, or tattoo it on your arm if you really like it! Now, which of the following things matches this description?"