Haley,
All other issues aside (with reputable artist, autoclaved instruments, sterile gloves, prophylactic antibiotics, close to good doctor, cardiologist's permission and knowledge, controlled air environments, inside you own home...)... Getting another authentic tribal tattoo in Bora Bora without any of the conditions described above sounds like a really terrible idea fraught with tons of risk and opportunity for infection.
I'm assuming you would be lying on the beach, exposing some skin to the sun (which you are not supposed to do with tattoos immediately after tattooing anyway) and sand and salt water.
All seems like really bad timing and very risky (and I'm a pretty adventurous person who isn't a worry wart).
I know you indicated you were going to abstain but I just thought I would reinforce with additional thoughts.
Have a good trip - and drink responsibly since you have coumadin now... Assuming of course drinking was part of the plan (I'm guessing because it would be for me...)
We all want to see pictures when you get back!