How to configure default keyboard layout in Kali Live

(I've asked this before in the abandoned installation forum, but that never got published/moderator-approved, so reposting here and hoping this is a better place.)
I've installed Kali Live successfully on a USB stick. Unfortunately it uses the wrong keyboard layout (US instead of Swiss German). No computer where I intend to use it uses the US keyboard layout, so I want to change that. I know how to change the layout in the UI or via command line ("setxkbmap -layout 'ch(de)'"), but I would have to do that after every boot and I want this to be configured within the Live installation.
I don't want to configure persistence (files and other settings), so I'm not using the persistence mode in the boot menu.
I know I could create a custom Kali image and make a stick that way somehow, but I think this is overkill for just the keyboard layout. I don't need additional packages or anything else.
I found that the configuration is stored in the file /etc/default/keyboard (at least it contains something like ="us" in there), but that file is not persisted of course. I assume this file is extracted from some archive during boot, so maybe I can modify it in the source somehow, if you have some more information about this.
I've seen that many other users have this same problem, but I found no solution so far, even after searching for many hours. This must be possible, because I've done it with the previous Kali version I had (several years ago), but unfortunately I don't remember how.
So how can I change the keyboard layout on the existing Kali Live USB stick?