As Jeppe Nielsen says in the other answer, the distance along the surface is not defined. I would tackle this visually so that the reader can convince themselves that your distance makes sense. Cut the protein in two parts (with a plane that goes through both of the active sites and the "center" of the protein). Then (in 2D) trace a path and measure its length.
Here is an example using xanthine dehydrogenase. Instead of cutting the protein, I used slabbing to remove the top part. This ensures an orientation where the plane is in the plane of the paper.
Using the linear distance shown as a scale bar, you can estimate the path length. This is all approximate, as it should be because the problem is ill-defined. If I choose a different orientation or slab, I will get a slightly different answer. You could also first select some surface atoms to define the path, and then estimate the distance by adding up atom-pair distances. Then, you could visualize the path in a 3D figure and state the distance.