Make salsa verde: Combine mint leaves, parsley leaves, and garlic on a cutting board and chop finely together. Transfer to a small bowl, add 3 tbsp. oil, the pistachios, and lemon zest and juice; stir well. Season with salt and pepper and set aside.
In a medium bowl, combine chopped mint, oregano, chives, thyme, and 2 tbsp. oil and stir together. Season with salt and pepper. Add fish and stir gently to coat evenly.
Using a vegetable peeler or mandoline, slice 1 zucchini lengthwise into paper-thin ribbons until you reach the core with the seeds, then rotate zucchini and repeat to cut more ribbons. Continue until only core with seeds remains. Discard and repeat with remaining 3 zucchini.
Heat an outdoor grill to medium-high (about 450°), or preheat a ridged cast-iron stovetop grill pan over medium-high heat. Have ready 6 metal skewers or bamboo skewers that have been submerged in water 30 minutes.
In a bowl, toss squash ribbons with remaining 1 tbsp. oil until well coated. Alternately thread halibut cubes and squash ribbons onto skewers, weaving each ribbon over and under to create a wave effect. Season loaded skewers with salt and pepper.
If using an outdoor grill, arrange skewers directly over fire. If using a stovetop pan, arrange skewers on pan. Grill skewers, turning once, until halibut has light golden grill marks, about 2 minutes on each side.
Transfer skewers to a platter or individual plates and accompany with salsa verde.