I was looking at the comments of other Ravelers who made these socks; some of them used ribbing in place of the picot edge. Of course, the picot edge is what gives the socks a really dainty look.
I don't know whether you could do both ribbing and a picot edge or not. If this is your first sock and you're fairly new to knitting, you may not be up for changing a pattern that much right off the bat. However, just doing the ribbing would be easy enough.