You would likely want fairly short circular needles if you want to knit the hat in the round. Say 16" or less, if you can find them.
To close the crown, you'll still need to use double-pointed needles, though.
Think of it this way: the number of stitches need to be able to fit totally on your circular needles - so you can close the loop, right? When you are stretching those stitches too hard to be able to knit the whole circle of stitches, then it's time to go to the double-pointed needles. So you can fit more stitches on the shorter circular needles because you'll still be able to knit the loop around and around. On the longer circular needles, your stitches would have to be enough to go completely around the bigger circle - so you'd need more stitches just to close the knitted circle.
Hope this helps,