I gave some more thought to your color changing problem. As I said I would cut the yarn each time and just start knitting with the new color. But if you happen to have a double pointed needle wide enough to work the scarf on or a circular you might try this. Work your 4 rows and then cut the yarn, move the stitches to the other end of the needle and begin with the second color in either knit or purl as the stitches present themselves ready to be worked. Keep doing that each time. This will cause all the tails of one color to be at one side of the scarf and the tails of the other color to be at the other end. That just helps to balance things out a bit and you don't have all the ends to work in on one side, so that one side feels thicker than the other.
Leave a decent tail each time and you might consider trying the duplicate stitch method of hiding in ends. It works nicely for something that will be seen on either side. Duplicate stitch end hiding.
Then pull on each tail as you get ready to work it in to tighten up any looseness and work the tail into its matching color stripe.
I have that book that the pattern is in. I looked it up again. Cute set. I had to look a couple of times to notice the 2 colors on the scarf, it looked solid color to me. Funny. Now I can't get it to look solid color since I finally saw the subtle difference in the 2 colors of stripes.