Hi chrisj,
I can tell you how to export from Cinema 4D, but to import into it should be discussed in the Unreal Forum, of course.
Please have a look here:
https://docs.unrealengine.com/en-US/WorkingWithContent/Importing/AlembicImporter/index.html
When I do precisely that, import the content into the Unreal [4.25] Context Browser as “Geometry Cache”, I get the Sweep object as animation into the scene.
I’m not sure if a Joint based setup (via FBX) would be here more appropriate. It depends on what you need. I assume the Unreal artists in the Epic-Forum have some ideas about it.
All the best