This is one of those projects where I wished I was more fluent in other software. I'm sure this would have been much simpler in an organice modeling package like Maya or ZBrush, but what I knew best was Solidworks, so I kept hitting this nail with the only tool I had until it did what I wanted.
First I had to split the sphere into two hemis because Solidworks does not like projecting onto infinite surfaces. Then, I had to sketch on multiple planes, project the sketches to the surface, and sweep geometries along them. Rinse and repeat a few dozen times to make the different sketches line up and look like a photo of an actual Snitch, and boom you have the winning Christmas present.