Is there anyway to wrap a slpine/curve around a surface in Solidworks?

I have a sketched spline I need to wrap around a roughly nautalis shaped surface.

I can only find an option for projecting a curve/sketch/spline onto a surface.

This option only projects the curve in a straight direction based off the orientation of the sketches planar surface it was created on.

And the resulting curve geometry is only of where ever the projected curve happens to interesct with the target surface in the direction of projection.

I have tried the Splitline option with identicle results.

Also I tried the the Wrap option under Insert/Features. It lets me select the curve I wish to Wrap and the Target surface.

The preview geometry appears correct, but then I get the "Rebuild Error"

"The Wrap feature cannot be created from intersecting or open contours"

So, are there any options for "Wrapping" a curve around or onto a surface?.

The sketched curve is a simple spline, tangent on each end to related geometry to where I need the wraped curve ends to end up. The start point is constrained to be on the end edge of the target surface. The sketch plane is offset from being tangent with the target surface, I tried this both ways, tangent  and not tangent, didn't make any difference. The dimensioned overall length of the sketched spline corresponds to the measured length of the target surface. The preview geometry looks great, just what I want. But the system cannot build it?