To make the kebabs:
Combine all the ingredients in a large mixing bowl and mix by hand just until all the ingredients are combined. If you have time, cover and refrigerate for 1 hour.
Take 1/3 cup of the meat mixture and form into a small log. Press the skewer into the log and seal the meat around it. Repeat with the remaining mixture.
Preheat a grill or grill pan over medium high. If you're using an outdoor grill, make sure to clean and oil the grates really well before cooking. Grill the kebabs 4-5 minutes per side until just cooked through.
To make the skyr sauce and serve:
Combine all sauce ingredients in the bowl of a food processor and blend until smooth. Season to taste with salt and pepper. Store in the fridge until ready to use. Transfer the skewers to a serving platter and serve with the herby yogurt sauce, fresh veggies, and lemon wedges.