Heat oven to 350°F. Line 24 cups of standard muffin tins with paper or foil cupcake liners; set aside.
In bowl of standing mixer fitted with paddle attachment ( or in medium mixing bowl using hand mixer), beat together cake mix, 1 cup coconut milk, sour cream, vegetable oil, eggs and lime juice until well combined. Stir in ¾ cups shredded coconut.
Evenly divide batter among prepared muffin tins, filling each cup three-quarters full. Bake, rotating pan halfway through, until tops are firm to the touch and thin knife inserted in centers comes out clean, 20-23 minutes. Transfer tins to cooling racks; cool 10 minutes. Remove cupcakes from tins onto cooling racks; set aside until completely cooled.
Meanwhile, transfer remaining coconut milk to small saucepan over medium heat. Simmer until coconut milk thickens and reduces to ¼ cup, about 10 minutes; set aside until completely cool.
In bowl of standing mixer fitted with balloon whisk attachment (or in medium mixing bowl using hand mixer), beat together cooled coconut milk, butter, cream cheese and lime zest on medium-high speed until smooth and combined, about 2 minutes. Reduce speed to low. Gradually beat in confectioners’ sugar until completely incorporated, occasionally scraping down sides of bowl with spatula. Beat in vanilla extract. Increase speed to high; beat until light and fluffy, about 3 minutes more.
Using small, offset spatula, spread cooled cupcakes with frosting. Or, transfer to large zip-top bag; snip off comer of bag. Pipe frosting onto each cupcake, starting at edges and ending with peak in the center. Sprinkle with remaining shredded coconut.