yungerman:
I do wash on a slice of pizza, and I don’t know what that has to do with a wrap.
I generally consider the issue of pizza to be whether cheese and sauce can make pas into pas kisnin, which the beur halacha says it cannot unless it is similar to hors d’oeuvres (meaning, made in small pieces for snacking purposes.)
One poster here said the issue by wraps is whether there is a toar lechem. I haven’t looked at that in a while. Perhaps you could say the same thing for pizza, but that I have never heard of, and then you would not wash even on more than a slice.