Trim any excess thick layers of fat from the pork shoulder and cut into large chunks.
In a small bowl, combine the sea salt, black pepper, ground cumin, and dried oregano.
Rub the spice mixture evenly over the pork pieces and place them into the slow cooker.
Add the minced garlic and pour the orange juice over the pork.
Cover and cook on low for 7 to 8 hours (or high for 4 to 5 hours) until the meat is fork-tender.
Remove the pork from the slow cooker and shred it using two forks, discarding any remaining large pieces of fat.
Optional: For crispy edges, spread the shredded pork on a baking sheet and broil for 3-5 minutes until golden.
Warm the corn tortillas in a dry skillet over medium heat for 30 seconds per side.
Divide the shredded pork between the tortillas and top with diced red onion, fresh cilantro, and sliced radishes.
Serve immediately with lime wedges for squeezing over the top.