The map projections you'll come across will (almost?) all be designed to take what is (approximately) a sphere and project it onto a flat surface. This will always give a distortion, but you can choose which type of distortion you prefer!
There is, naturally, a wikipedia article on this:
Map projection - Wikipedia, the free encyclopedia
However, in your case, you'll be "projecting" a sphere onto a particular 3-dimensional surface (shoulder/arm).
I don't necessarily have a particular suggestion - just wanted to make sure you were aware of the various issues involved here... (e.g. taking a spherical projection onto a flat surface, and then wrapping it around a another 3D surface may not be optimum.)