Hi Rippart,
Your Stellar wallet doesn't need to have anything, when you send a transaction to an exchange with a wrong memo the exchange still receive the funds, the only difference is that they can't route the deposit to the correct user. If you remember the memo you used you can still send them that. Also get your wallet address and go to www.stellarchain.io and check the history of your transactions you should be able to find the transaction there.
Thanks