Rub the pork shoulder evenly with cumin, oregano, garlic powder, sea salt, and black pepper.
Place the seasoned pork in a slow cooker and pour the orange juice and lime juice over the top.
Cover and cook on low for 8 hours or on high for 4 hours until the meat is tender and easily pulls apart.
Remove the pork from the slow cooker and shred it using two forks, discarding any large pieces of fat.
Heat a large non-stick skillet over medium-high heat. Add the shredded pork in a single layer and sear for 3-5 minutes without stirring until the bottom is crispy and golden.
Warm the corn tortillas in a dry pan or over an open flame for 30 seconds per side until soft and pliable.
Thin the Greek yogurt with a splash of water or extra lime juice to create a crema consistency.
Assemble the tacos by dividing the crispy pork between the tortillas, then top with diced red onion, cilantro, and thinly sliced radishes.
Drizzle with the yogurt crema and serve immediately.