Pour cherries, with their juice, into a glass bowl. Cover cherries with rum. Cover with plastic wrap and store in the refrigerate for 1 week.
Drain and dry rum-infused cherries.
Line a baking sheet with waxed paper.
Mix confectioners' sugar, 1/2 cup butter, milk, and maple syrup together in a bowl until smooth and pliable. Wrap each cherry with sugar mixture. Arrange on baking sheet. Cover loosely with plastic wrap and chill until firm, about 30 minutes.
Combine chocolate chips, semisweet chocolate, 2 tablespoons butter, and paraffin wax in a saucepan. Heat over medium-low heat, stirring, until melted, about 5 minutes.
Dip each wrapped cherry into the melted chocolate mixture using a toothpick. Return to baking sheet. Repeat with remaining cherries. Cover loosely with plastic wrap and chill until set, about 1 hour.