Preheat the grill to medium-high.
For the Cajun dry rub: Combine the salt, black pepper, chili powder, cumin, granulated onion, paprika and cayenne pepper in a small bowl.
For the spicy peach bbq sauce: Drizzle the Anaheim chile with canola oil and season with salt and pepper. Grill until charred on all side, about 5 minutes total. Cool briefly, and then remove the stem and chop.
Put the bacon, onion and garlic in a small saucepan over medium-high heat and cook, stirring occasionally, until the onion is translucent and the bacon is slightly caramelized, about 5 minutes. Stir in the peach preserves and Anaheim chile, then stir in the barbecue sauce, molasses, rum, cider vinegar, Dijon mustard, 1 teaspoon salt and 1 teaspoon black pepper. Bring the sauce to a boil, then reduce the heat and simmer until the sauce is slightly reduced and thickened, about 10 minutes. Cool; put the sauce into a blender and puree until smooth. Divide the sauce among 2 bowls, reserve one for serving.
For the prawns: Line a serving platter with the arugula. Drizzle the prawns with the oil and dust with the Cajun dry rub on all sides. Grill until charred on the first side, about 3 minutes. Flip the prawns, baste with some of the spicy peach bbq sauce, and cook until the prawns are charred on the second side, about 2 more minutes. Baste, flip, baste again, and pull off the grill.
Put the shrimp on top of the arugula and serve immediately with the reserved bowl of spicy peach bbq sauce on the side.