If I were a doctor, I think I would be more prone to recognize a "NO CODE" bracelet over a tattoo. A tattoo is a decision you made on a single day. Wearing a bracelet is a decision you make every day of your life.

(Of course, you could say that leaving the tattoo in place is a decision you make every day, but it's much easier to remove a bracelet if you change your mind, vs. a tattoo.)