There is a better way! You will need a circular needle to use for this kind of flat work. Knit one row in the first color. Slide the stitches to the other end of the circular needle. You are still working from the right side of the garment. Knit a row with the second color. Turn and purl a row with the first color. Slide the stitches to the other end and purl a row with the second color. Turn and knit next. Keep working that way, knitting two rows from the right side and purling two rows on the back side, sliding and turning as needed to have the next color at hand.
Thanks so much for the quick reply, too! Trying to do some Christmas knitting for for each of 8 grandchildren, so every day counts. This is the first time I’ve come to “KnitHelp” - what a great site!