Never lie back and take any form of reprimand or punishment you feel is unjust. Fight it all the way, whether leaving or not, and make sure the union finally do something to justify their fees.
No need to be nasty about it, stay professional and be sure of your ground and the disciplinary rules which your employer has to abide by. People seem to forget that this process is binding on both parties. Ensure all of your fellow crew members provide written witness statements for the investigatory stage of the process confirming their support, and ensure this is brought up should the company wish to proceed to a full disciplinary hearing.
If your notice period expires as soon as you say, then either the company will drop the matter as a futile waste of their time and resources, or you can extend the process up to and beyond your leaving date. Either way you will leave with no formal disciplinary record, and the company will have to state as much should a future employer (as some do) ask for this information.