Mediterranean Chicken Kabobs with Yogurt Sauce (Grill or Oven)

Yogurt marinade and sauce
2 Whisk [wprm-ingredient text="½ cup thick plain yogurt" uid="1"], [wprm-ingredient text="¼ cup tahini paste" uid="2"], [wprm-ingredient text="2  tablespoons extra virgin olive oil" uid="3"], [wprm-ingredient text="2 tablespoons fresh lemon juice" uid="4"], [wprm-ingredient text="2 tablespoons cold water" uid="5"], [wprm-ingredient text="2 teaspoons grated or finely chopped garlic" uid="6"], [wprm-ingredient text="1 teaspoon ground cumin" uid="24"], [wprm-ingredient text="1 teaspoon dried oregano" uid="23"], [wprm-ingredient text="¾ teaspoon kosher salt" uid="11"] and [wprm-ingredient text="¼-½ teaspoon  cayenne pepper" uid="12"] and in a bowl until smooth. The sauce can be made up to 3-5 days ahead. Keep it refrigerated until ready to use. If it thickens as it sits, stir in cold water, a few teaspoons at a time, to reach a thick, spoonable consistency. 
Assemble and cook chicken skewers
12 To ensure everything on the skewer cooks evenly, cut [wprm-ingredient text="1 ½ pounds boneless chicken thigh or breast" uid="9"], [wprm-ingredient text="1 medium zucchini (about 10 ounces)" uid="14"], and [wprm-ingredient text="2 red, yellow or orange bell peppers" uid="22"] into chunky 1-1/2-2-inch slices. Keep the tomatoes whole. 
6 Put the chicken pieces in a large bowl and toss with ½ cup of the marinade, a good pinch of kosher salt, and black pepper to taste. Marinate the chicken about 15 minutes at room temperature, or refrigerate up to 6 hours ahead.
5 About 15 minutes before you're ready to cook, preheat a grill to medium-high heat (about 375F or 190C) for direct grilling. If you're cooking the skewers indoors, preheat the oven to 450 degrees and line a large rimmed baking sheet (or two medium ones) with aluminum foil.
7 Thread alternating pieces of chicken, zucchini, tomatoes and bell peppers on skewers. Aim for about 10 total pieces per 12-inch skewer. Drizzle about a teaspoon of olive oil over each skewer.
8 Grilling: To prevent sticking, get your grill nice and hot before putting the skewers on the rack. Put the skewers on the preheated grill and cook until the chicken is cooked through, 3-5 minutes per side. If they're browning too fast, move to the cooler part of the grill and cover to finish cooking. Baking: Arrange the skewers on the prepared baking sheets. Bake 20 minutes, turning once halfway through, until the chicken is no longer pink and the tomatoes are bursting.When the meat feels firm and has no trace of pink inside (internal temperature should be close to 165 degrees), they're done.
To serve
11 Spread about ¼ cup of the yogurt sauce on a large platter. Arrange the skewers on top and sprinkle with the feta cheese and cilantro. Squeeze the lemon wedges over and serve with additional sauce on the side.