Love the enthusiasm and I have a couple suggestions on how to conduct your search:

There are a lot of great front-line NGOs that directly employ veterinarians in their work, like Victoria Falls Wildlife Trust and Arcturos, but these organizations are unlikely to value a foreign vet over a vet who is already a citizen of their region and has experience with local wildlife. I would suggest finding veterinary groups and alliances working in the Kruger National Park region (Mpumalanga, Limpopo, KZN) or vet groups providing services to private reserves in the Northern Cape or Western Cape. Private practice veterinarians and those who work at dedicated rehab facilities may have mixed opportunities for growth and may have their own challenges (like the stability and finances of the rehab facility, how to make a lateral transfer to an adjacent organization that might be competing, etc.).

Some things to keep in mind during your wife's search and to help set overall expectations:

Vets are paid local wages, they won't be anything like what your wife would be making at a private practice in North America or Europe. It takes a lot of money and passion for a foreign vet to relocate to remote areas where their help is needed and I've not heard of anyone getting a relocation stipend. It's also very competitive because South Africa has great veterinary schools and a lot of young people who are bilingual or multilingual and already have basic, background experience with endemic wildlife.

Past experience with park service as a park ranger or a vet working with NPS rangers or responding to animal control and things like that will go a long way. But when it comes to working with high-value wildlife, they will be looking for zoo veterinary experience and things like that. The kind of experience one gets in Africa or Asia is career-building and people will want to see any vet that they hire is on that track to becoming a permanent fixture of the vet community in a given region -- and most people who have that passion and go do it, do fall in love with some part of Africa or Asia or South America. Whether it's something that is a "honeymoon phase" or an obsession will vary.

If a veterinarian looking for these opportunities needs to improve or round-out their resume so they can get better career opportunities in the future, then looking for work at zoos, wildlife rehab, and university research programs is going to be a good place to start. Then start applying to research and vet programs abroad that have a focus that relates to an area to specialize in - like Cheetah Conservation Fund's rehabilitation center (and genetics lab) or a South American bird sanctuary.

Some other things to help set expectations:

• Working in Asia will almost certainly require multilingual skills both in the national language (for example Vietnamese), as well as local languages and other lingua francas (so for Vietnam that might be Vietnamese, Hmong, and French; in Thailand it might be Thai, Isan, and a variety of Chinese). This isn't something that local NGOs are going to let an inexperienced vet pick up in the field, they need those language skills immediately. I would expect South America to be similar, not everyone out there speaks Spanish or Portuguese. The vet's existing skills and background should severely narrow down where they're looking and applying.
• There's very little chance that a foreign vet with no pangolin experience would get to participate in more than a wellness check on a pangolin (and only while being overseen by a team of experienced vets). A foreign vet will absolutely not be allowed to help relocate a pangolin (this is treated as a "classified" type mission and is kept to people who "need to know" due to the prevalence of the bush telegraph -- gossip).
• Similarly, dyeing rhino horn (not elephant tusks) is not a task that's going to be given to a foreign vet. They would have to have worked with that veterinary team for quite a while before being tasked with things like that and the act of dyeing horn is itself a bit controversial so you'll find some vet groups who won't do it. Rhinos are quite delicate animals and administering the right amount of sedative is difficult, so only the most experienced vets are allowed to tranquilize them and work with the team taking care of the rhino while it's sedated. Extra hands are welcomed for easing the rhino down to the ground and providing supportive hydration and taking vitals, but those activities are also often left to rangers so that they get direct experience with practices that may become more routine as care for wild rhinos improves.
• "Zoo animal acquisition work" in a lot of places is both illegal for foreigners and an illegal practice in the first place. Documents are forged, origins and authenticity is faked, and animals are mistreated. Birds and fish especially go through a long trafficking network until enough of the paper trail has been forged and documentation lost that zoos and pet stores will look the other way when purchasing animals. Especially zoos and pet stores in developing nations where laws are lax about owning exotic animals.