For anyone seeing this, I fixed the degenerate triangle problem.
At first I thought it was my character that had degenerate triangles. But then I noticed that stepping over a specific area in my environment was causing the issue. I managed to narrow it down to a spawning asset that I have in my level where every time my character stepped on it the degenerate triangle message would appear.
I looked online to see what tools I had avaliable to clear degenerate triangles. Blender has a tool in Edit Mode for meshes that allows you to clear degenerate triangles. So I imported the asset into Blender and immediately noticed another problem: the asset was incredibly small. Tiny even. This was the crux of the problem: the asset had triangles that are way, way too small. Sure enough when I scaled the asset up and tried to clear degenerate triangles in Blender, it said 0 cleared.
I exported the scaled asset in Blender and imported it again in my UE project. When I imported it, the entire mesh was bigger than the environment I was in. Looking at the blueprint showed that it had a scale of 50.
I took the scale down to 2.5 and the issue is now solved.