Using a larger needle size will give you more drape. It will also make the cowl larger of course. What yarn does the pattern suggest?
A nice soft worsted that I like is Caron Simply Soft. I haven't used it in years, but as I recall it had great colors, too!
I agree with not using RHSS. It may get slightly softer when washed, but it'll never be really soft. Also it hurts my hands to knit with it. :zombie: RH has another yarn called SOFT and that one is really soft.