Sometimes it's really hard to find things on here using the search tool...!
has a great selection of Malabrigo
yarn, if you want wool. It's merino and not itchy at all, I LOVE it! She has a ton of colors, call or email her, they aren't all on the website.
Silk or silk/cotton would be good.
Bamboo is as soft as silk and less expensive. I've used South West Trading Co.
and it's lovely. Very lightweight, so it would make a thin hat and you'd be using smallish needles. Knitting Nook has that, too.
Also, I've heard lot's of recommendations for Blue Sky
, seems almost all of their yarns would be nice. Lot's of people said the cotton one would be great.