Is it safe to unload the Spineboy and RaggedySpineboy textures after the repack process? Yes.
Is it safe to unload the AtlasAssets after the repack process? It should be. It doesn't do anything except hold a bunch of references.
And the AtlasAsset is really only used when the Skeleton is first loaded. All the pertinent data is stored in SkeletonData and each Skeleton itself.
If you're doing something super customizable, you may just be better off with using Sprite assets instead of getting parts from atlases. That will save you the step of having pack custom parts through Spine.
But yeah, after the skeleton is deserialized, it should be safe to unload the original loaded atlas and texture.
If you run into any problems or notice anything, do let us know!