For the parts and their variants, it will probably come down to how flexible you want to be with mixing and matching different styles of parts, or if you could see having more set limitations to what you can change to at once. I say this as knowing and planning that would determine how you will setup your textures, to atlas or not to atlas, etc.
For how the textures are handled, if there are no set limitations and you can literally wear variant parts from a bunch of styles, one for each body part (or anything else), I would recommend just creating a single texture for each body part that can be interchanged. Then just make variants textures from then on, so you’d have Legs_V01, Legs_V02, etc, then just hot swap textures via code on that particular Polygon2D node when the player chooses what to wear.
If there are some set limitations for the player, or just in general there are not going to be many variants to worry about, I’d say set up an entire style set on one texture sheet, then make the other styles in the same way, just make sure the layout is the same, then for each Polygon2D body part you just hot swap in code the style texture on that particular part the player changes a variant on.
If you don’t have more complex setup needs for the Polygon2D nodes, like making the verts and polygons on the shape be specific to the texture sprite, or more detailed deformations. I could see where if you had a Polygon2D node for every variant part it could get to be more of a hassle and burden on the character setup/scene, and rely more on resources like textures, materials or custom resources (highly recommend using these as you could put a lot more gameplay info in the part resource, beyond just the texture you swap).
This gets complicated pretty fast 
For the wings, I could see just adding those bones to the existing skeleton, including the Polygon2D node and just doing the enable/disable trick again. This would lean into the idea of using the same Polygon2D body part nodes for all style variants as then you are more free to add specialy bones to the same skeleton, then just enable/disable the parts as needed.
On the animation side I don’t know if that could cause a problem if you play a non-walk cycle animation on a character where you enabled the wing parts, especially if that walk cycle animation didn’t include the wing bones when it was exported (and vice versa for that matter).