You could combine that Wrap you are attempting with some cloth simulation to achieve this? EDIT: Also, wrapping in the sense you are after would not work in that case without distorting the geometry a lot or ending up with strange folds.
Does anyone have a technique that they would recommend for producing a believable animation of a character wrapping a bandage? I had been considering using an elongated plane rigged with a chain of bones, then unrolling it over a character's arm. My plan would be to export this for use in UE4.