Place half of the coconut milk, garlic, soy sauce, and lime juice into a resealable plastic bag. Seal the bag and shake well to combine the marinade. Add the chicken strips, squeeze the bag to coat them evenly, and refrigerate for at least 3 hours. Set aside the remaining coconut milk.
Preheat the oven to 400°F (200°C). Line a baking sheet with aluminum foil and lightly grease it with olive oil.
Pulse the shredded coconut in a blender or food processor a few times until finely ground. In a bowl, combine the ground coconut, panko crumbs, salt, and black pepper. Place the flour in a second bowl and the beaten egg in a third shallow bowl. Remove the chicken from the marinade, letting any excess drip off. Dip each chicken strip first into the flour, then into the egg, and finally coat it with the coconut mixture. Arrange the coated chicken strips on the prepared baking sheet.
Bake for about 30 minutes, or until the chicken strips are golden brown.
In a small saucepan, heat the reserved coconut milk with the mayonnaise over medium-low heat until it simmers. Serve the sauce drizzled over the chicken or as a dipping sauce on the side.