Soak 8 wooden skewers in cold water for 30 minutes.
On a cutting board, using the flat side of a chef's knife, mash the garlic and salt to a coarse paste. Add the caraway seeds and finely chop them. Transfer to a large bowl and stir in the chile powder and olive oil. Add the shrimp and toss to coat.
Meanwhile, slice the chorizo into 1/2-inch rounds and lightly fry over medium heat for 5 minutes. Drain and pat dry. Let cool slightly.
Tuck a chorizo slice in the crook of a shrimp and thread onto a skewer; the shrimp should be attached at both ends. Push it to the end of the skewer and repeat with 3 more shrimp and chorizo slices. Using more skewers, repeat with the remaining shrimp and chorizo.
Grill the kebabs over medium-high heat, turning once or twice, until charred and the shrimp are cooked through, about 5 minutes. Serve immediately.