Assuming it's not okay for me to just present the players with a list of skills they can roll, have them roll, and then narrate what happens based on the success or failure of the roll...
Well, I think the section on Skill Challenges is poorly written. I don't think the authors intend that you present any such list to the players. You, the DM, have a list of skills that you feel apply. You don't present that to the players any more than you present the stat blocks of all the monsters they fight.
Like in a fight with a monster, you describe the situation, and the players get to try anything they wish. They describe their actions - some of them will match things on your list, some won't. But, if hey may suggest a method of approach that you didn't think of that you think is valid, you can accept that as if it was on your list, and adjudicate the results on the fly. Rather like if they'd thought of a combat tactic you didn't.
Consider the list to be guidelines, and it's all good.