Cotton might be a weird choice of yarn for a project like this. But it has to be natural fiber and washable. I considered superwash merino but I am afraid that the process which makes wool superwash might be problem here. So cotton it is.
On the other hand I might have used completely untreated fiber… but how to wash them?

I began with the stripes part, it looks quite cool in the blue-blue colour combination. Slipped stitches form narrower stripe than I expected though. Photo later.

I decided to knit the stripped part until I ran out of the pale yarn and then finish it with the darker one, possibly in some ribbing, depends on how much will be left.

Modifications: started as M size, made 18 stripes. In next row I added one stitch for every 4 sts (k3, kbf all over). Ribbing for the end: k3 p2.

… then I went overboard with the modifications. I added a crochet bind off in the light blue colour. Two rows of crochet. And from the bit of remaining yarn I made two tassels. LOL. Anyway the shawls is bathing now in vinegar, I’ll leave it there for the whole night. Then it will be blocked and dried, properly photographed and sent to the recipient.

Note: in the end the tassels haven’t made it into final version.