For the slaw: Whisk together the ketchup, red wine vinegar, celery salt, kosher salt, black pepper and cayenne in a large bowl. Add the cabbage and toss to combine. Cover and refrigerate for at least 1 hour and up to 24 hours before serving. Taste for seasoning just before serving.
For the crabs: Heat a charcoal or gas grill to high heat direct grilling. Brush both sides of the crabs with oil and sprinkle with salt and pepper. Grill until the crabs are just firm to the touch, 2 to 4 minutes per side, depending on the size.
For assembly: Place 1 large or 2 small crabs on the grilled buns, top with a large spoonful of coleslaw and 2 slices of tomatoes. Serve immediately.