Do you have access to the EA account tied to the swtor account ? if you do you can change the email on the EA account see this link
from there see if you can remove the security key per this link
If all else fails a quick call to CS (Link) they will be able to sort this out for you
Edit - I am aware that there was/is hotmail/outlook mail server issues if relevant and maybe why there has been no emails
I dont know whats linked or not but this account im posting on is the EA account and i changed the email on my EA account. No idea if thats linked or related to my swtor account or not
I changed my EA email but nothing seemed to happen.
For example, if you switch the email address on your EA Account, you’ll also need to confirm that change for SW:TOR by following the steps to validate the new address (you should receive these steps by email).
The only email I got was to confirm my new EA email but nothing about swtor itself
