ANSWER
DI-α-Tocopherol is fat and oil soluble and insoluble in water. However, a liquid phase of Dl-α-Tocopherol is somewhat dispersed in water. The common antioxidant and preservative for coconut milk is sodium metabisulfite (Aramouni & Deschenes, 2014; Longbotham & Schaeffer, 2012; FAO, n.d.).
Another proposed antioxidant is sodium ascorbate, which is powder form of ascorbic acid (Vitamin C) with neutral taste and soluble in water (Igoe, 2011).
References
Aramouni, F., & Deschenes, K. (2015). Methods for Developing New Food Products: An Instructional Guide (pp. 114-5). Lancaster, Pennsylvania: DEStech Publications, Inc.
FAO. (n.d.). dl-α-Tocopherol.
Igoe, R. S. (2011). Dictionary of Food Ingredients, Fifth Edition (p. 127). Berlin: Springer US.
Longbotham, L., & Schaeffer, L. (2012). Luscious Coconut Desserts (pp. 1-13). San Francisco: Chronicle Books LLC.