I come from a similar background as you (MPH international health and development) and spent the last 8 years working in global health programs in DC before going back to school for my FNP and a complete career re-route.
Please do careful research into jobs available once you're done. I have and there are VERY few opportunities, as advanced practice nursing is not recognized internationally. If you've got colleagues at the CDC, start connecting with them to find out if they accept nurse practitioners. You might find yourself up against MDs, who ARE internationally recognized, and passed over.
You can certainly go the project management route, but keep in mind 1) your clinical skills may not get used AT ALL. (this is what drove me from the field and you'll be frustrated as you see your fellow clinicians, especially international colleagues, go from being valuable members of the healthcare system to managers pushing paperwork); 2) you certainly don't need a clinical degree (and the $80,000+ in debt you'll go into for it); and 3) funding is drying up in international development at an astonishing rate. Especially for HQ-based staff, as they are moving most operations out to the field where qualified locals can (and should!) be doing the jobs that used to be done by us expats.
Network, network, network. Find the people who have jobs you want and talk to them. Find out who else is doing them.
TL;DR: What specialty do I recommend? Probably NONE of them.
Best of luck!