Can I use a mesh with ShapeKeys or MorphTargets?

The process of rigging a mesh with Uefy Script requires applying the armature modifier to the mesh. Blender does not allow this if the mesh has shapekeys. You will need to delete the shapekeys to rig the mesh.

You can create new shapekeys after rigging is complete or you can try to copy/transfer shapekeys to the rigged mesh from a different object. However this is a complicated process that might require custom scripting. Refer to StackExchange and Unreal Forum for examples of how people have done this.