We do this all the time where I'm at, because we have to show seat sensors wrapped onto the foam of a seat.
1) Extract the surfaces that you'll be mapping to.
2) Use the plane of your section to create a rectangle that encompasses your section, and is parallel/perpendicular with it.
3) Intersect the surfaces with the box.
4) Do section curves through the trimmed surface sheet, at regular intervals (perhaps adjust later based on surface quality, and how your system behaves).
5) Use those sections to create a single Through Curves surface.
6) This is the 'wrapping' step. With Project Curve, use the Projection Option of 'Equal Arc Length'. This will maintain the x and y lengths of your original section, as it maps down to the single surface (it only works with a single surface - I'd love UG a lot more if it could go to a surface sheet). The reason for the box, and the surface method, was to keep the u and v lines perp to each other, so that it maps correctly. This should work great for your task, but it can easily fail if you're mapping to something with a lot of sharp direction changes.