A Curve can be projected onto a surface and then machined quite easily in the Mill Professional. The one thing to look out for is compensation of the tool using wireframe in 3D.
I think your second approach would result not only in a safer more controlled program but will allow you to machine the model rather than the wireframe projected onto it.
In the XP Series Mill Expert we have a new function that allows you to "apply" (which differs from project) a custom wireframe toolpath onto a model that is then examined in relationship to the surfaces and the cutter being used. A "groove" depth can then be defined as part of the CAM Wizard for that function. It differs from the existing function by doing a tool to model comparison and behind the scenes NURBS interaction.
However the Mill Professional will accomplish this task for you easily.
(see attached final part image fo reference)
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