It is possible for the global shortcuts in the dedicated GUI.
Is it possible for the custom shortcuts too?
A similar option as above is not present in the KDE4 GUI for custom shortcuts.
But I imagine there must be some file to back-up.
The custom shortcuts seem not to be saved as an overall scheme, but as separate groups of shortcuts.
In the Custom Shortcuts window select Edit - New group, if you don't have one or more already.
Check to enable the group and then drag&drop the shortcuts you already have onto the group.
To save a group, right click on it and export:
~/.kde/share/config/kglobalshortcutsrcthere are different sections, and the[khotkeys]one might be what you are searching for. It should then just be a matter of changing said file to your likings.~/.kde/share/config/kglobalshortcutsrc. If you prefer I can edit my answer myself and just give credit to your comment.