SerjChey How can I export each skin to a separate png file
This wording doesn't make sense. Skins are stored in the skeleton data, which is JSON or binary. If space is a concern, use binary. The skeleton data always contains all skins, Spine doesn't support partially exporting a skeleton.
SerjChey then in the browser receive from the server only the skins I need and not all the texture atlases that take up a lot of space and load the network
You will always have all the skins in the skeleton data. That is fine, they don't take up much space.
To pack a texture atlas with a PNG containing the images for each skin, place your skin images in subfolders. See here:
At runtime, instead of AtlasAttachmentLoader, you can use your own AttachmentLoader that doesn't require all the PNGs to be loaded when the attachments are created. Before you can render your skeleton, you'll need to configure each attachment the skeleton will need for rendering using your texture atlas. See here:
Also see the source for AtlasAttachmentLoader, as that is what you need to do, just only for the attachments you care about.