I don't understand the very straight line across the front.
Is this your hairline?
Plus, it being on paper means that its 2D.
If you made a traditional template then it would be 3D and fit the contour of your head.
If you send that in, the piece you'll get back will misshape in exactly the same way as if you were to try and get that piece of paper to lay flat to your head.

But maybe this is just an example and not the actual template?

Removing a section like this from a topper wouldn't/shouldn't present any problems or ruin the remaining hair.
You would simply place the template (topside up) against the underneath of the lace base, draw around it and then with a sharp blade, and no pressure, slice along the drawn line, cutting just the lace & not the hair.
As Paul says, with the remainder, you could repeat this again, possible even 2 times from one standard topper.
Although in my opinion, the subsequent sections would be a compromise and inferior to the first piece.
Ok for an emergency or if you never revealed your hairline.