Engraving tool paths PERPENDICULAR to a curved surface

Hello
First sorry if I am asking a silly question , but I am new to this.
I am using rhinoCam now to engrave some curves on a curved surface(4 axis machine). The problem is thet the tool engraves perpendicular to the xy plane and I need the engraving to be perpendicular to the surface. I am not sure how can I do this.

Probably easiest to cut on centerline in Y (or X) and movement in X(or Y) + 4th if you need to make any depth of cut or tool length adjustments at the machine.

If most of movement is 3d with occasional 4th reposition, depth adjustments become a trig problem - either need to be done in cam, unless you're using 3d comp? I bet most people don't though.

Shouldn't be that much slower using the 4th than 3d milling. Unless you're using a spindle speeder and going super fast.

Personally, I'd use a 1/32 or .8mm ball, and now that I think about it I'd program the tool with a slight tilt to cut more on the side, isntead of the tool tip. Use TCPC, so rotary motion on the 3+1vmc or 5axis machine.