Hello misaki_m!😃
Why do you set different skins for the same appereance of the character? Or, since you can't key a skin on the timeline, do you mean a skin placeholder or an attachment, or maybe multiple attachments?
If you mean that you prepare in setup pose alternative attachments in the same slot for each part, then I guess it's the right approach. If you look at the gif frame by frame you can easily notice that they moved the parts a little, swapped them completely in a frame, and reflected an equivalent of the root (never reflect the root! reflect the first bone inder the root if you must) two frames later, moving a little the parts in the process. If you need you change draworder and then you take it back to the correct order. I think you wrote it down well yourself for the most part.
To ease the activation/deactivation of alternative attachments you could prepone the view to their names, such as:
front-head
front-body
side-head
side-body
so that if you filter the tree by attachment it's easier to find them and activate them.