One solution I prefer in games like these where you don't really want to skip all the cutscenes all the time is if you press any key (or some predefined keys), than a timer starts (circle starting to fill up, etc.) and if the timer finishes you skip the cutscene. It could be around 3-5 seconds. It would also be quite natural on touchscreen devices.
If the story is still about a boy and a girl on a journey, they could meet at the end of the world (location), while the world is ending around them. Oh and i just love ice levels in any game:)