Preheat a grill to medium heat.
In a bowl, combine the lime juice, oil, 2 teaspoons of the ginger, garlic, and pepper flakes. Add the shrimp and pineapple chunks, toss to combine, and let marinate while the grill heats, about 15 minutes. Remove from the marinade.
Wrap the shrimp with the prosciutto. Alternately, thread the pineapple chunks and the wrapped shrimp onto metal or bamboo skewers. Grill until the shrimp are cooked through and the pineapple chunks are marked, 3 to 4 minutes per side. Remove from the grill. (Alternately, the skewers can be cooked under the broiler, turning as necessary to cook evenly and avoid burning.)
Make the sauce in a medium saucepan by combining the rum, shallots, and remaining 2 teaspoons of minced ginger. Bring to a boil. Reduce the heat and simmer until reduced to 3 tablespoons in volume, 3 to 4 minutes. With the heat on medium-low, whisk in the butter, 1 tablespoon at a time, adding each piece before the previous one has been completely incorporated. Continue until all the butter is incorporated and the sauce coats the back of a spoon, removing the pan from the heat periodically to prevent the sauce from getting too hot and breaking. Season with the salt and cayenne, and stir. Remove from the heat and transfer to a decorative bowl.
To serve, transfer the wrapped shrimp and pineapple chunks from the skewers to a platter. Sprinkle with the cilantro and serve with the rum butter sauce.