A profile API for custom player head items/blocks has now been added: https://hub.spigotmc.org/stash/projects/SPIGOT/repos/bukkit/commits/04c7e13cf0fb199cce3db3ada646b4bd61a57580

However, modifying the profile (e.g. skin) of a player entity is not yet possible.

A player profile api could also be very useful to create custom player heads (that do not use a real players uuid/name, but only a textue stored on mojangs skin servers) or to create a head from a stored player profile to avoid mojang lookups.

Isn't that hard to do yourself. I actually made a plugin out of it (https://www.spigotmc.org/resources/beta-multi-character.78441/)

(Feel free to remove comment for shameless selfplug)

reregistering the player works, remove player and then add player with a respawn packet if im not mistaken.

I've been looking at how setting a skin would be achieved with NMS code so that this could be implemented in the API.

I've tried setting the player's skin URL to another in the GameProfile PropertyMap and then sending a PlayerInfo packet.

getHandle().playerConnection.sendPacket(new PacketPlayOutPlayerInfo(PacketPlayOutPlayerInfo.EnumPlayerInfoAction.ADD_PLAYER, getHandle()));

But haven't seen much success, it doesn't seem to change the skin if the player already has it cached on their client?

I don't want to sign the CLA, mainly cuz I don't want to dox myself. 
Some1 who already has access I'd like to make it. Thanks

Sure. I don't see why that can't be proposed at least as a PR. Though that String argument will have to be documented thoroughly much like we've done with resource packs (see Player#setResourcePack())

Sure, then we add Player#setSkin ??

Then instead API for changing a player's skin should be added but wrapping the player profile in an API seems unnecessary to me. There should be a proper layer of abstraction around this rather than just letting developers access the profile and potentially break something they should not be. Even a Player#setSkin(String) or Player#broadcastSkinChange(String) would be more appropriate here.

I can't agree with you Choco. What if I am making a minigame and want to change the skin of the player?

This isn't necessarily something we want to expose. Unless, of course, md_5 believes otherwise - though as far as I'm concerned this is an implementation detail that plugins should not be capable of modifying.