Can I fake being in the customizer?

You don’t need to fake being in the customizer, just grab the theme mods directly via get_theme_mods. Afterall they’re just theme specific options.

Something like this would print out all the theme mods in a definition list:

function tomjn_print_theme_mods() {
    $mods = get_theme_mods();
    if ( empty( $mods ) {
        return;
    }
    echo '<dl>';
    foreach ( $mods as $k => $v ) {
        echo '<dt>'.esc_html( $k ).'</dt>';
        echo '<dd>'.esc_html( $v ).'</dd>';
    }
    echo. '</dl>';
}

https://codex.wordpress.org/Function_Reference/get_theme_mods