I think you won't get good geometry with shrinkwrap. Also the skin modifier works completely different (see https://www.blender.org/manual/modifiers/generate/skin.html). You rather would use shrinkwrap to put labels onto surfaces and similiar things.

I opend your stl file and it is really a mess geometry wise. Can you tell how this was created?

I think the best would be to rebuild the mesh.

I think you won't get good geometry with shrinkwrap. Also the skin modifier works completely different (see https://www.blender.org/manual/modifiers/generate/skin.html). You rather would use shrinkwrap to put labels onto surfaces and similiar things.

I opend your stl file and it is really a mess geometry wise. Can you tell how this was created?

I think the best would be to rebuild the mesh.

Edit: Maybe my answer was a bit misleading or even wrong regarding the usage of the shrinkwrap modifier. If you would do a retopology of your mesh you would use the shrinkwrap modifier for the workflow (see tutorials on youtube).

I'm not sure what you want to archieve. I made a .blend with a working (?) shrinkwrap on your mesh.