Season the pork shoulder thoroughly with ground cumin, dried oregano, sea salt, and black pepper.
Place the seasoned pork in a slow cooker and pour in the orange juice, lime juice, and minced garlic cloves.
Cover and cook on the low setting for 8 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 excess large pieces of fat.
Heat a large non-stick skillet over medium-high heat and add the shredded pork in a single layer.
Press down with a spatula and cook for 3-5 minutes without stirring until the bottom is golden and crispy.
Warm the corn tortillas in a separate dry pan or over an open flame until soft and pliable.
Divide the crispy pork between the tortillas and garnish with thinly sliced radishes, chopped cilantro, and finely diced white onion.