In a large mixing bowl, combine the tuna, cucumber, carrots, peppers, tomato, onion, and chives. Gently toss with hands. Season with the salt and lime juice. In the piece of cheesecloth, add the grated coconut. Then gather up the ends and over the bowl, wring out the milk from the coconut by twisting the cheesecloth tighter and tighter; retain the coconut juice for another recipe (notably Prawns with Vanillla Coconut Sauce, also shown on this show). Gently toss the ingredients in the bowl again and serve immediately.