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.
RH has another yarn called SOFT and that one is really soft.