Hi!
It is possible to create any “rig” you want, and reuse them, you can also edit them. In the content browser, right click on the skeleton → Create-> Rig
There is an other asset that you may need, the BoneMapping. In your skeleton, once you have assigned a rig and set matching bones, there is the save button just below the rig selection. The same thing for this asset, you can edit the mapping itself later.
You can also try to set the retargeting to “skeleton”. On top of the bone hierarchy in the skeleton, there is a button “options” then “show retargeting options”. You will see on the right of each bone the translation retageting, you should try to set on “skeleton” at least for the legs.