Special equipment: six 10- to 12-inch wooden skewers soaked in water for 10 minutes; or metal skewers
For the shrimp: Preheat the grill to medium-high heat.
Mix the pineapple juice, lime juice, spiced rum, rice wine vinegar, brown sugar, ginger and garlic in a small saucepan. Bring the mixture to a boil. Mix the cornstarch and 1 tablespoon water in a small bowl. When the juice mixture comes to a boil, whisk in the cornstarch slurry and whisk until thickened, a couple of minutes. Remove from the heat.
Place on each skewer 2 pieces of pineapple, 2 shrimp, 2 pieces of red bell pepper, 2 pieces of yellow bell pepper, 2 pieces of onion and 3 mushrooms. Season the skewers with salt and pepper.
Oil the grill. Place the skewers on the grill and brush with the glaze. Grill the skewers on each side until the shrimp is pink, 3 to 4 minutes, brushing with the glaze halfway through.
For the mint chimichurri: Add the mint, olive oil, rice wine vinegar and red onion to a bowl; mix well. Season with salt and pepper (heavy on the pepper). Serve with the shrimp skewers.