A few points to consider regarding your desire to participate in overseas cleft surgery:
Perhaps twenty years ago, any plastic surgeon would be welcomed to perform cleft surgery, because cleft surgery was considered one of the basic operations of the specialty. However, in recent years, those plastic surgeons with craniofacial fellowships have mostly succeeded in limiting cleft surgery to those with a craniofacial or cleft or pediatric plastic surgery fellowship. So, it's most likely that you would not only need to do a plastic surgery residency to do cleft surgery abroad, but a craniofacial fellowship as well. Even then, you might not be able to find an opportunity to do surgery abroad, since there are generally more surgeons willing to go overseas than there are places on trips. In fact, the politics in many of these organizations is quite fierce. That's why these organizations proliferate. The senior people in each organization keep a tight reign on who gets to go on trips, and on which trips. If you're not part of the inner circle, one of their associates, or from their university, you won't be selected. So, frustrated plastic surgeons then start their own organizations. There are also groups that center around other medical specialties, such as ophthalmology. Many other trips treat general surgery problems. There is a group of OR nurses in my hospital who organize an annual trip to the Phillipines every year, and the physicians on that trip treat a wide variety of surgical problems. Of course, if you follow the news, you know that there is a need for primary care and infectious disease specialists overseas as well.
While plastic surgeons do almost all of the cleft lip surgery, many other procedures are done on a variety of trips with various organizations.
Even on a trip devoted to cleft lip surgery, there are opportunities for non-plastic surgeons to participate. In fact, surgeons will make up a small minority of the participants. You could participate as a pediatrician, an anesthesiologist, a nurse, a scrub tech, as a lay person providing administrative support, or as a translator. As a physician, you would generally have to pay for your own airfare and expenses. If you are serving in a non-physician role, more of your expenses might be covered.
As an aside, be aware that in many countries that these organizations visit, there are local plastic surgeons capable of doing the surgery. What is lacking is not so much the doctors, as the money. In many third-world countries, not only is the patient responsible for paying the doctor and the hospital, but they have to buy their own medical supplies: IV tubing, syringes, saline, antibiotics, etc. So it's the poor people that are treated by these organizations. The wealthy and the middle class can be teated by the local doctors. For example, some of these organizations have trips to Vietnam. I have been to Vietnam, and had occassion to visit one of the hospitals there. It was on par with most of the hospitals I have worked in in the US. It was staffed entirely by physicians who rotated out from France. They had CT scanners, MRI scanners, private rooms, and very attentive nursing staff. But, it was very expensive. It catered to the very wealthy. or those who had relatives abroad who could pay the bills. It's like when you read about famine that kills thousands of people. It's not that there isn't any food around. There's usually a lot of food, otherwise, the journalists who report the story would starve to death. Rather, food has become too expensive for the poor, who barely get by under normal conditions, are priced out of the market, or can only afford half of what they would usually eat. So, if you do go abroad on these trips, be aware that in many of the countries you go to, you will not be providing services that are unavailable in that country, although they will be otherwise unaffordable to your patients. That said, there are some countries where specialists really don't exist. In those instances, there are opportunities to not only perform surgery, but also to teach new techniques to local doctors. But you don't have to be a plastic surgeon to be of use overseas.
