100% Confirmed by Myself:
The Swtor Key Authetincator also comes in a Smartphone App. The App is free and if you link your account, you can buy the 2 Customizations offered on Ilum Orbital Station.
It's not actually on Ilum, to clear confusion, but rather the space station before you jump down to Ilum itself.
...but yeah, just go get the app for your smartphone and you can buy them. Unfortunate for people without smartphones : /
My issue with this is; what happens if something unfortunate happens to my iPhone (it's getting old, I worry about it sometimes).
Can you get the app, buy the stuff you want, then unlink your account again? I am very careful with my acct info and stuff, after MMOing for 15 years and never being hacked, so I am not terribly interested in the security part.