Hello,
If you still have access to your email address and your password, you might be able to remove the security key without contacting the support team.
If you go to the swtor website ( swtor.com) and only enter your username and password, and leave the security key field empty, a new window should appear asking you to enter your security code, but on that same page, it would normally show " security key lost?", if you click on it, it will ask you if you want a One time password to be send to the email address linked to your account, and that will allow you to remove the security key :
https://help.ea.com/en/articles/star-wars/star-wars-the-old-republic/security-key/
However, if you don't have the password, or if you are not getting the one-time password, then you would need to contact the SWTOR support