It's very difficult to convey fuzzy, short hair in pixel art. One of the things that lends itself much better to traditional media then any digital media, really.
It is going to be difficult for ANY of us to make convincing fuzz.
As far as I see it (and my scope is limited, take note

), he's got two choices:
1) He makes a noisy, dirty fur, like he has here
2) He makes a clean, edge based fuzz. This will read more clearly as fur, no doubt, but it's not going to lend itself to realistic shading at all.