Your math would have a hat that fit loosely without opening the ribbing at all, no negative ease. I like loose hats but that would blow off in a strong wind.
The pattern doesn't say what size it is, only "adult or child". There is no way that hat would fit on my 24" head.
I would figure 21" for the hat to fit that head. 168 stitches. That would also work out for the 2x2 ribbing because it divides by 4.
Knit a few inches and try it on, with DPNs you probably have to knit almost to the decreases to get an idea if it will fit.
Once you change the stitch count you're also going to have to change the decreases, so that whole pattern may as well be thrown out the window for everything but the color and 2x2 ribbing.
Use this, http://www.thedietdiary.com/knittingfiend/tools/knittingHat.html
You may have a problem with the cast on being too tight. What I do is cast on too many and decrease the first round. Cast on 252 stitches and decrease every other stitch while working in pattern, K1, K2tog, P1, P2tog.