If you look at the give well job description for a research analyst (http://www.givewell.org/about/jobs/research-analyst) it doesn't mention that GiveWell is interested that people who apply have a degree.

If that's where you want to go applying directly to GiveWell would be the straightforward course of action.

Given FHI's academic nature they probably do prefer people with degrees but I think FHI doesn't want specific degrees but wants to hire people with expertise that they currently don't have so they should be pretty open.