I am pretty sure tattoo ink is different from pen/marker ink. As long as the pen or marker is nontoxic, it probably won't hurt you (although if you're worried, you can always ask the artist to forgo a ballpoint for a "tattoo pen," which is specially formulated for drawing on the body and tattooing over).

This link is a good explanation of tattoo inks, and how they aren't really "ink" at all, but pigments in a carrier solution.