I made another cute cat yesterday, but I can't get a good photo of it because it was made in very dark fiber. I may have to try some new lighting arrangements and see if I can finally get a decent photo.
There are several ways to reduce the amount of surface fuzz on a piece.
When you begin finishing a piece the best technique is to use #42 needles at a very shallow angle AND positioned so that the first barb (which on a #42 is on the same side of the needle as the bend in the L at the top) is the first to enter your piece. I call this "Surface Felting" - your needles are almost parallel to the surface of the piece. This helps to catch a lot of those flyaway fibers and secure them into the piece.
Once a piece has been properly surface felted you may still find some flyaway fibers - it's pretty much the nature of the craft - and then your best tools are a sweater (or fuzz) shaver, or fine scissors.
When using a sweater shaver, do not apply heavy pressure on the piece. Sweater shavers are capable of shaving off more than you really want. You just want it to glide across the surface so that it can shave off those flyaway fibers and give your piece a nice neat finish.