Prepare the grill for direct cooking over medium heat (350° to 450°F). If you're using a charcoal grill, keep a small part of the charcoal grate clear of briquettes as a safety zone of indirect heat.
Lightly brush the potato halves with oil, and then grill over direct medium heat, with the lid closed, until a fork slides in and out easily, 30 to 40 minutes, turning three or four times. If the potatoes begin to turn darker than golden brown, finish cooking them over indirect heat. Remove from the grill and let cool slightly.
When cool enough to handle, use a small knife or the edge of a spoon to cut around the cut side of the potato to within ¼ inch of the skin. Scrape off and discard any charred sections of potato. Using a spoon, scoop out the interior of the potato, leaving a shell about ¼ inch thick attached to the skin. Place the potato pulp in a large bowl. Set the potato shells aside while preparing the stuffing.
Using a potato masher or the back of a fork, mash the potato pulp in the bowl. Add the sour cream and mix well. Stir in half of the cheese and all of the remaining ingredients. Taste the potato mixture and, if desired, add more wasabi, salt, and pepper. Spoon the potato mixture into the shells, mounding it slightly. Top the potatoes with the remaining cheese. Adjust the grill for indirect cooking over medium heat (350° to 450°F).
Grill the stuffed potatoes over indirect medium heat, with the lid closed, until the cheese is melted and the potatoes are heated through, 10 to 15 minutes. Serve immediately.