I've made LOADS of the chemo caps based on the Lion Brand pattern. Always use the large pattern for adults. The microfiber yarn makes them VERY STRETCHY! Remember also that we are usually measuring our heads WITH HAIR. The 16" is perfectly fine and comfortable for those without. Don't pull the stitches too tight. Knit easy.
If you are planning on making a number of them I would definitely invest in size 13 DPNS and do them on those. It makes the decreasing and finishing off of the cap so much easier. I've also done them on straight needles, but it can be tricky to do the mattress stitch right in order to sew them up because of the fun fur.
Also, always buy 2 of the fun fur skeins for each cap. They seem to vary in amount from color to color and I wouldn't want you to run out.
Good luck with the caps and good luck and much love to Grandma.