Preheat oven to 375°. In a large bowl, cream shortening and sugar until light and fluffy. Beat in eggs and lime juice. In another bowl, whisk flour, pudding mix, baking soda and baking powder; gradually beat into creamed mixture. Stir in pistachios and dried cranberries. With clean beaters, beat egg white on medium speed until thick and foamy; stir in coconut.
Drop dough by rounded tablespoonfuls 2 in. apart onto ungreased baking sheets. Flatten slightly with bottom of a glass dipped in sugar. Top with coconut mixture. Bake until until edges begin to brown, 10-12 minutes. Remove from pans to wire racks to cool. Sprinkle with lime zest. Store in airtight containers.
Test Kitchen tips
If the coconut shreds are too long, chop them up before mixing them with the egg white. This will ensure that the whole cookie is covered with coconut.