I expect they change needles sizes so the cables don't pull in so much. I think I'd pick one size needle to use on the whole scarf. Or if you feel you must, just go up one needle size. Any more then that you'll be struggling too much to even knit from the smaller needle to the larger, I don't want to think how hard the crossing stitches will be!
It's such an unusual thing to do - in the book is there a written paragraph or two about the scarf? do they discuss why they change sizes? No tips how to make the crossing doable, let alone easier? I think if I designed a cable that way, I'd make a comment about why I did it. In any case, it must be so the cables aren't pulled in too much - that's the only reason I can think of to do it.