Yes on the alternative. That’s what I do with my HD 560s. I plug the 6.35 female to 3.5 male adapter into the Sonata HD Pro first, then connect the dongle to my source and finally plug the 6.35 male end of the 560s cord into the female end of the provided adapter.
No need for 3.5 to 3.5 adapter for the HD 560s since it already requires an adapter to use with 3.5 ports.