Soak wooden skewers in water for 30 minutes.
In a medium bowl, whisk together gochujang, soy sauce, honey, sesame oil, minced garlic, and grated ginger to create the glaze.
Reserve half the glaze in a small bowl for basting later. Toss the shrimp with the remaining glaze and let marinate for 15 minutes.
Thread the marinated shrimp onto the soaked wooden skewers, about 4 to 5 per skewer.
Preheat grill to medium-high heat (about 400°F) and lightly oil the grates with olive oil.
Grill the skewers for 2 to 3 minutes per side. Baste the shrimp with the reserved glaze during the last minute of cooking until opaque and slightly charred.
Arrange a bed of baby arugula and sliced radishes on a serving platter. Place the hot skewers on top, then garnish with sliced green onions and toasted sesame seeds.