I don't know if this will help you or not, but I knitted a chemo cap for a family member. I used a LionBrand pattern. I tried to link the pattern but I think they are having trouble with their website. I will try to find it again later. But if you search on the LionBrand wesite for "chemo cap". It should come up. There are a few to choose from. The one that I used was HOT PINK and fuzzy. It used fun fur yarn. I hope this helps. It was knit on straight needles and then a seam up the back.
Every hat i've knitted, which is about 20, I only do with straight needles.
Your basically knitting a rectangle. Whatever size you need. Then you start decreasing (k2tog or P2tog) for a few rows depending on the amount of stitches you have. When your done decreasing you take your yarn needle, thread it with the yarn your knitting with, start slipping the stitches onto it and when you get to the last stitch pull that thread through and secure the top. Your done. Below is an example of my hat pattern.
Rows 1,3,5,13,15,17: P1 WYIB SLIP 1P, P1
Even Rows 2 - 24: Purl
Rows 7,9,11,19,21,23 P2 WYIB SLIP 1P, P1 end last repeat with P2
Row 25: *K1 K2tog* across row
Row 26: Purl
Row 27: *K1 K2tog* across row
Row 28: Purl
When you have the size hat you want then,
Cut yarn, thread the yarn needle through the stitches and pull it through to form the crown of the head. Secure the top with a stitch and stitch the side up.
Tip; You want to decrease on the right side rows only so it doesn't show from the front.
If you already have a pattern that you like, you can easily convert it from circular or dpns to straight needles. Simply add a stitch to the beginning of the round and to the end of the round. Then knit the first stitch before referring to the instructions and when you get to the end of the round, knit the last stitch.
If the pattern is complicated, like lace or something, you might have to do a swatch or two, but it should work out.
Spokaloo is correct. You can even use a circular needle, just turn your work at the end of the round like you would when knitting a cardigan.
Depending on how you want to sew it up add a stitch to one of both ends of the round if using a back stick seam. If you are good at sewing up with mattress stitch or if the hat is a slightly looser fit, you won't need to add any stitches. Just remember purl every second row (i.e. stocking stitch) instead of knitting every round. No need to change needle sizes.
Believe it or not although I have knitted quite a few hats, I have never knitted a hat in the round.