Unfortunately the problem is that different Mixamo skeletons, while they can use the same bone hierarchies, have different bone transformations to put the skeletal meshes in the same base pose. This is the reason you can’t simply “swap” the skeletons.
In addition, you can use options to generate different bone hierarchies (mostly about fingers), that complicates the subject further.
For now it must be managed as a normal animation retargeting problem.