Heat the olive oil in a large nonstick skillet over medium-high heat. Add the sausages and cook, turning, until browned all over, 6 to 8 minutes. Add 1/4 cup water, cover and cook until the sausages are just cooked through, about 2 minutes. Transfer to a plate to cool, then slice into 2-inch pieces.
Reduce the heat under the skillet to medium; add the butter and caraway seeds and cook, stirring, until the butter is melted. Add the fennel and apple and cook, stirring, until slightly softened, about 3 minutes. Add the sauerkraut and sausage slices and cook, stirring, until the sauerkraut is warmed through, about 3 more minutes. Season with salt and pepper. Top with fennel fronds.