Since you're not using a pattern, your best bet would be to make a gauge swatch to see how many stitches you get to an inch. Knit a square a little more than 4" wide and 4" long. Then you can measure how many stitches you need to get the width you want.
That's the 'correct' way.
What I would probably do is look at some kid's patterns to get an idea of how many stitches they call for to cast on for a hat his size and go from there.
It's really up to you. You know best what you can do and how willing you are to mess up once or twice.
"Trust the pattern!"
Time flies like an arrow, but fruit flies like a banana.
Hop aboard while we follow the cloud-covered van of knitting harmony, man!! Woooo!! --Hedgehog
IngridKH on Ravelry