Existence of lists doesn't imply possible anything. Choosing is an action independent of being listed. One does not need the statement of what one can be what one might do to do so. He must be capable of doing it. If he is capable of doing it he will do it regardless of whether he is also capable of doing other wise.
The capability for doing otherwise does not signal choice of doing so is an option. It only signals one has the capability to do this or that. Since determinism states one does this then that that is what one does. You have not shown that one has the faculty of choice. You've just shown that a determined one is capable of doing this or that which is not contrary to what determinism states. One does this then that regardless of capability.
You might look at things this way. One has encountered this and that so the capability to do this and that exists. However when this arrives that is determined. Otherwise one would need to know whether this or that were signaled. Obviously that was signaled since that was the result. You need an intervening uncaused variable, implied not evident, to do otherwise. A nonexistent cause to do otherwise is needed.
The deterministic cause of the choosing operation is our encountering a situation where we are faced with two or more real possibilities and we cannot go forward without making a decision. Thus, the list of options on the restaurant menu, and the social expectations of the waiter, are the prior causes that necessitate our choosing.
So, the choosing is deterministically caused to happen. Within the choosing operation we experience certain thoughts and feelings that will follow one upon the other in a deterministic fashion. We will see the Steak dinner on the menu, recognize it as a real possibility, and experience a desire. Then we will recall our bacon and egg breakfast and our double cheeseburger lunch. Then we will recall our doctor's recommendation that we eat more fruits and vegetables. Then we will see the Chef Salad on the menu, recognize it as a real possibility, recognize that it satisfies the doctor's advice, and tell the waiter "I will have the Chef Salad, please".
If someone asks us about our choice, we can explain why we chose the salad rather than the steak. "I could have ordered the steak, but I already had bacon and eggs for breakfast and a double cheeseburger for lunch. So, I decided I would order the salad instead."
The "could have" refers to the point in the choosing process when we recognized the Steak dinner as a real possibility, something that we could have chosen if we wanted to.