To make salsa: Mix persimmon, lime juice and hot sauce in a bowl. Season to taste with sea salt and fresh ground black pepper. Cover and refrigerate for at least 1 hour, so flavors can infuse. The salsa can be made 24 hours ahead and kept in the fridge. Bring to room temperature before serving.
To make marinade: Mix tequila, lime juice, olive oil, garlic, onion and spices. Marinate the shrimp in this for an hour, tossing them around regularly.
To grill shrimp: Remove the shrimp from the marinade, season with salt and thread onto skewers (wood or metal). Keep the marinade to brush the shrimp as they grill. Cook on a hot grill for about 2 minutes each side, brushing with the marinade once or twice per side.
To serve: Spoon salsa on a plate, arrange shrimp skewers next to it and garnish with cilantro and mint.