Hi, I don't think either paper melts into the icing and completely disappears; the border is always going to be visible on either one, unless you submerge the edges of the paper in the icing (which can get messy). Also, wafer paper does not take well to wet icing AT ALL - it will curl and buckle on you - so if you are going to press the paper into the wet icing, you need to work with frosting sheets. The downside of that, in my opinion, is that the frosting sheet becomes more integral to the cookie, and frosting sheets are very thick and a bit weird texturally to eat.
I have a video (Edible Papers 101) that talks about the different handling characteristics of these papers. You might want to check it out: http://cookieconnection.juliau...ip/edible-papers-101