Unfortunately, if your shell script is not part of the sandbox, a change must be done at the Sigil code level and would be completely specific to flatpak (and not on our list of things to do).
Flatpak's sandbox approch has similar issues with other Qt KDE editors like Kate that use things like plugins, use external apps of the user's choosing, ... just like Sigil.
The KDE solution is to remove Kate from flatpak completely since it would need too much help and support for what they called "broken sandbox model" of flatpak.
See the full discussion here:
https://bugs.kde.org/show_bug.cgi?id=431223
Perhaps Sigil should follow the same approach as Kate since the flatpak version of Sigil will not be able to use "Open With" to open external apps of the user's choice, not be able to use Plugins/java, not be able to run PageEdit as XEditor, not be able to open external browsers under flatpak. This is true because neither the default tmp folder for edited files open in Sigil and no commonly available user apps that people might want to use typically live in the user's /home directory which is the only place the sandbox has full access to.
Just building your own Sigil on Linux would be a much easier and simpler way to use the latest versions of Sigil on older Linux systems.