In a bowl, toss the peeled and deveined shrimp with Cajun seasoning until they are well-coated.
Heat olive oil in a skillet over medium-high heat. Add the seasoned shrimp and cook for about 2-3 minutes on each side until they are pink and opaque. Remove from heat and set aside.
Meanwhile, in a separate bowl, combine the green cabbage, red cabbage, grated carrot, and chopped cilantro.
In a small bowl, whisk together the mayonnaise, apple cider vinegar, lime juice, and season with salt and pepper. Pour the dressing over the cabbage mixture and toss until everything is well combined.
Warm the corn tortillas in a dry skillet for about 30 seconds on each side.
To assemble the tacos, place a few shrimp on each tortilla and top with a generous amount of slaw.
Serve with lime wedges on the side for an extra zest.