Creating a 3D concave shape, without a border

I am a glassblower, and I want to carve various 3D concave shapes into some cherry wood. I have chunks of cherry, that are no particular size. I would like to just zero my x-carve in an open area of the wood plank, and start to remove the shape, without it cutting a border.

Is there a way to easily do this? I have created both the positive shape (but this has borders, since I had to remove it from a solid, and then I created a solid model of just the part of the shape that would be removed.

I dont totally understand how to i can tell the machine to cut the shape, but dont do any borders or things…

I hope makes sense. I have trouble putting the thoughts in my head to words.

Recently saw in England that a glass blower had set his piece, while red hot, directly onto various wood shapes, root balls etc., and the hot glass burned a shape into the wood giving the work a very unusual and rather beautiful display stand.
If you are loading an STL file into your CNC, try doing a model boundary relief with 0 padding on all four sides.