I decided to go with the "All Players" option for the new skins. I made an attempt to have only players in the ZfH Steam Group have access to custom skins, but this caused the skin to switch back to the default after every map change or disconnect. The last thing we want are server settings requiring more attention, by having to manually add new players for who can use which skins.
If I can find a way to automate this using the Steam Group (without bugs) then we will change to that in the future.