I'd say more so the 'customisation skin' options in Vanilla or the 'offline skin' mod (forget the name of it but something along those lines) would suit but that's just my guess, otherwise don't think one exists for skins when it comes to texture packs as texture packs/resource packs are more for the game's assets textures, not the players skins. Sorry if that's not the answer you were expecting, but it's what sounds likely to be the case to me with what texture packs are known for and what they actually do.
'Niche Community Content Finder' for fun and support of creators. I just swim through my 'Experimentation Pond' of content that intrigues me or really needs a bit of acknowledgement or bug fix testing/reporting. I also make modpacks/maps
Creator/Maintainer of Fabric, Rift & Tesla Mod Discussion Threads/Niche Mod Youtuber.