Cut the tuna into 8 equal-size cubes. Combine the sherry, soy sauce, oils, rice vinegar, wasabi paste, ginger and garlic in a bowl. Reserve 1/3 of the marinade for dressing the vegetables later and add the tuna cubes to the 2/3 remaining. Marinate for 1 to 2 hours, refrigerated.
Remove the stems from the mushrooms and cut them into quarters. Thread the tuna unto the skewers, alternating with the mushrooms, two pieces of tuna and two mushrooms per skewer.
Using a food slicer, julienne the cucumber and daikon radish into pasta-like threads and mix with the red pepper julienne. Dress the vegetables with the reserved marinade and allow to marinate for 20 minutes before serving.
On a hot outdoor grill or under a broiler, sear the kebabs for two to three minutes on each side. The tuna should be medium rare still red in the center. Serve the grilled skewers on a bed of marinated vegetables.