I dislike how the entire skills system was removed from Fallout 4, but I hope it might be possible to bring it back in a mod.
I was wondering that maybe certain private integers can be linked to the player object. These integers could represent values pertaining to the old skills:sneak, big guns, science, medicine etc... These integers would have set and get functions with a sanity check(like it being greater than 100 or less than 0). Maybe a custom menu could open within a few minutes of a player gaining a level allowing the player to add values to these integers. The perk chart (aka Vault-Tec approved perks) would be linked from a special menu(by clicking on a option) containing perks like the originals.
I do not know that much about Papyrus but it looks like it has all of the primitive types available. I am only making assumptions so take this with a grain of salt.