I meant the old .exe would check the signatures before initializing the official Windows way to update. Effectively have this run whenever you start the application:

main() {
    if (update_available()) {
        exe_path = download_update()
        if (signature(exe_path) == SIGNATURE) {
            install_update(exe_path)
            restart()
        } else {
            put_up_a_warning_or_something()
            delete(exe_path)
        }
    }
# Rest of the application
# ...
}

The only thing I have no idea how to implement would be the install_update(path) function. But surely this is one way to install updates without signatures recognized by Microsoft, right?

And if for some reason you aren’t allowed to sign the .exe because this breaks something, then place an unsigned .exe in a signed zip folder.