If a time traveler wants to be as inscospicous as he could get, tattoos are not a good idea. Tattoos tend to identify customs, likes, and cultural thought constricted to a particular time. Thus they might endanger a group of time travelers. Imagine going back in time to the Middle Ages sporting a brand new blood dropping chain around your wrist. The Church would have a blast. The same holds true for future traveling, in which the traveler knows nothing about the culture he/she will be encountering.
So my honest opinion is to refrain from getting tattoos if you are planning to be hopping on a timeship soon! You could get the removable (temporary) ones, no one will know!