How Can create a Sweep with normal to projection as centre axis

I want to create a groove on a cylinder as shown in the image. I create the groove path and wrapped on the cylinder

I am using sweep to create the groove, if i select normal to trajectory the sweep cut is created on cylinder. but for manufacturing i want to create the cut normal to center axis.

if i choose normal to projection and select ctr axis sweep feature failing. It will be helpful if anybody can suggest a solution.