I already found a solution to this without using the email customizer. The plugin actually doesn’t use the translation that does actually exist in the localization files.
In fluid-tracking-info.php, line 154:
<a href="<?php echo esc_url( $tracking_item['ast_tracking_link'] ); ?>" class="track-button" target="_blank"><?php esc_html_e( $fluid_button_text ); ?></a>
Needs to be replaced by:
<a href="<?php echo esc_url( $tracking_item['ast_tracking_link'] ); ?>" class="track-button" target="_blank"><?php esc_html_e( 'Track Your Order', 'woo-advanced-shipment-tracking' ); ?></a>
Now it grabs the correct translation, which the other parts of the tracker also do.