To be frank, for the 60 quid, I would but the peace of mind, cancel the first ticket for a refund, and purchase a new ticket on SU. This is because SU is not confirming to you that it has anything booked for you in any manner.
Nobody here can say with any certainty that there won't be a list done and if there is, you will have spent 60 you need not have. But, it all just sounds dodgy and is a matter of risk tolerance.
If you show up on the appointed day and ask for your boarding pass and are laughed at by SU, you will have the choice of not traveling or purchasing a ticket at the walk-up price.