Angora Chemo Hat Question

A friend of mine is wanting to knit a chemo hat with angora yarn.
It needs to fit snug and hold it’s shape. This will be just a cap, no brim or anything. It is just for warmth or as a liner for another hat.

Will it stretch and not hold it’s shape?

it should
I ahve made flowers that turned out horribly due to it having to much Give
and I am making a Shrug that (it turns out) will need to have a LOT of give in the end
I will cry if its to rigid

just kick up a size, not a few just one
JMHO, not total experience YET