You could try a lighter weight yarn (around 20sts/4" instead of 18sts/4" called for in the pattern) and smaller size needles with the same instructions given in the pattern. That'll make a smaller hat. It doesn't have to be too much smaller as you can see from this chart
Even if you use the yarn weight called for, do a gauge swatch with your yarn and needles and you'll be able to calculate the number of sts to cast on for the hat size you need. Remember to knit the hat slightly smaller than the actual head size so that it isn't too loose but fits comfortably.