cold portalYou can’t make a layout truly uneditable, but you can make it hard to change by shipping it in a modpack with FancyMenu’s modpack mode enabled: set modpack_mode=true in /config/fancymenu/options.txt. That hides all overlays/hotkeys so players can’t open the editor, even though FancyMenu still runs (needed to load your layouts).
And yes—you must keep FancyMenu in the game instance after you port the menu. The mod is required at runtime for those layouts/resources to load; copying only the configs without the mod won’t do anything useful.
More on shipping layouts in packs and modpack mode: Modpacks documentation.