The tiny preemie hat is 10 1/2 inches around I think and the biggest hat I think was 14 or so inches. 84 stitches seems like quite a few, but she is using small yarn. The two smallest hats are in baby yarn or fingering yarn. That is similar to sock yarn and it quite fine. The others are made of sport weight which is a step up in size but smaller than worsted. Sport weight works up to around 22 stitches for 4 inches and worsted it more like 17, but they all vary, and of course it depends on the needles you use.
I suppose it is possible to make the hat flat and put a button on it to close it. When it says to join it to knit in the round, don't-- just work back and forth. If you need the edges to overlap a bit for a buttonhole you might need to add a little for that, or you could put a loop right at the edge and maybe not need more stitches.
I've not made this hat and don't know what all other changes you might need to make, but you can probably figure it out.