Beat the heavy cream in a large bowl with a mixer on medium-high speed until stiff peaks form, about 3 minutes. Fold in the cream of coconut until just incorporated.
Spread about 1 heaping teaspoon of the coconut whipped cream onto each gingersnap. Press the cookies together on their sides to form a 12-inch-long log on a serving platter. Cover the log with the remaining coconut whipped cream. Cover with plastic wrap and refrigerate at least 6 hours or overnight.
Preheat the oven to 350 degrees F. Spread the coconut flakes in a single layer on a baking sheet and bake until just golden, about 5 minutes. Let cool completely.
Peel, pit and dice the mango. Toss with the lime juice, sugar and a pinch of salt in a small bowl. Sprinkle the toasted coconut all over the cake, gently pressing to adhere. Top with the mango. Cut on the diagonal to serve.