Came back after 4 years: i need to remove the authenticator
There are only two ways to remove an old security key as you cannot add a new one till the old one is removed.
The first is manually by going to swtor.com and go to log into your account. Enter your Display Name and Password but leave Security Key empty and then click Login. On the next screen it should ask for your security key, below the security key field is a link that says "Forgot your security key?" and then you can click on that to receive an email to remove the security key. See this article here under the section "What do I do if I lost my security key or can't access it?" for screen shots and more info.
The second method is by calling swtor customer service. You may have called them outside their hours of operation but their contact info and hours are found here. If you have Skype, WhatsApp or another VoIP program, you can call for free or at a discounted rate if needed.
