In a medium bowl, whisk all of the salmuera ingredients together. Season generously with salt and pepper. Divide the salmuera in half; reserve half for dressing the salad.
In a small bowl and using a fork, mash the yogurt and feta until smooth. Season with salt and pepper. Alternatively, puree the yogurt and feta in a small food processor until smooth.
Light a grill and oil the grate. Skewer the cherries, leaving a few inches on either end for handling. Season the steak with salt and pepper. Grill the cherries over high heat, turning and basting with some of the salmuera, until lightly charred, 5 minutes. Transfer to a plate. Grill the steak over high heat, turning once and basting with salmuera, until charred and medium rare within, 6 to 7 minutes. Transfer to a cutting board and let rest for 10 minutes, then thinly slice the meat against the grain. Remove the cherries from the skewers.
Smear the feta yogurt on the bottom of a large platter. Arrange the arugula, grilled cherries, and sliced skirt steak on the platter. Drizzle with some of the reserved salmuera and sprinkle with snipped chives.