From the summit of the Schwarzhorn there are two options: either down climb or rappel the class 4 west of the summit, or back track down from the summit and traverse the southwest face of the Schwarzhorn. Either one can be very tedious, as the exposure on the class 4 is very harrowing, and the traverse is over loose rock on another steep slope. Once you gain the ridge, head east and stay close to the top of the ridge. The ridge is mostly class 2 with some bits of class 3. Soon you'll come to the low spot on the ridge and the ascent begins. Focus on the summit of the Grauspitz. It IS NOT the peak closest to you with the cross on it. The Grauspitz has no cross. The peak with the cross is the Sammi Claus. Soon you'll come to a secondary summit, and from there the summit is about 2 minutes away. Re-trace your steps back. The class 4 back up to the summit of the Schwarzhorn is much easier to go up than down, so if you feel comfortable with it, ascend the class 4. It is much more enjoyable than doing the traverse again. The rocks is a little loose, so watch your footing. Time from the Schwarzhorn to the Grauspitz is 1/2 hour.
A good map (which can be purchased at the Älpli Bahn), good grippy boots, water. If you so choose, I think a 60 meter rope would be sufficent for the rappel from the summit of the Schwarzhorn. Again, pro isn't neccessary, but if you are uncomfortable on class 4 with decent exposure, it would be a good idea to be prepared.
"When a true genius appears in the world, you may know him by his sign, that the dunces are all in confederacy against him."