Move, rotate, and constrain a copied (under-defined) spline without changing spline shape

I have copied a spline from the face of a part, then pasted it into a sketch in my current part.  I want to retain the spline shape for joining later, once I complete my current part.  I have used the move and rotate functions to get the spline close to where I want it without changing the shape or size of the spline, but now I would like to put it in its final position using constraints.  Is there a way to fix the shape of the spline such that my constraints simply move and rotate the spline rather than modifying the spline?

I would like to move the spline entity to the left such that the small radius on the right is constrained tangent with the solid line from that other sketch.  If I simply just select the two and constrain tangent, it changes the shape of the under-defined spline.  I can't simply define the spline since it came from a face that was extended against a plane at an angle to the extrusion direction, and so I can't just create a defined spline with dimensioned control points.  Is it possible to do what I'm asking?

SolidworksSketching