Rub the pork shoulder evenly with the ground cumin, dried oregano, sea salt, and black pepper.
Place the seasoned pork into a slow cooker along with the orange juice, lime juice, and minced garlic cloves.
Cover and cook on low for 7-8 hours (or high for 4-5 hours) until the meat is tender and easily pulls apart with a fork.
Remove the pork from the slow cooker and shred it using two forks, discarding any large pieces of rendered fat.
Preheat a large non-stick skillet over medium-high heat and add the shredded pork in a single, even layer.
Press down with a spatula and sear for 3-5 minutes without stirring until the bottom of the pork is brown and crispy.
Warm the corn tortillas in a dry pan or over a gas flame for 30 seconds per side until soft and pliable.
Divide the crispy pork between the tortillas and garnish with finely diced white onion, chopped cilantro, and thinly sliced radishes.