Oh, I see. That does challenge my usual conception of identity more than my initial interpretation.

In essence, then, this is asking if I would choose to sacrifice myself in order to preserve myself. I believe that I like myself enough to do that. If my exact brain-state continues onward while the "original" experiences the pain, my identity does diverge, but it does so after I make the choice to press the button. In that sense, my identity continues, while also being tortured. The continuation, given its time span, seems ultimately more important when considering the alternative of ceasing to exist altogether.