Line an 8-by-8-inch pan with plastic film.Select 64 whole nuts and set aside. Pulse the remaining nuts in the processor until finely ground.
Heat the cream and 1/4 cup rum in a heavy saucepan over low, swirling occasionally, until small bubbles rise.
Remove from the heat, add the white chocolate and stir until smooth, returning the pan to a very low flame if needed to melt the chocolate completely. Stir in the ground nuts.
Pour half the mixture into the lined pan and spread evenly.
Arrange the whole nuts in an 8x8 grid over the surface of the chocolate. Sprinkle the fleur de sel over the whole nuts.
Carefully spread the remaining half of the chocolate over the nuts with an offset spatula. Cover with plastic film and chill until firm, 4 to 6 hours.
Invert the chilled chocolate onto a cutting surface. Cut into 64 cubes, centering a whole nut in each one. Roll each chocolate cube into a ball between your palms.
After all of the balls have been formed, stir together the butter and remaining 2 tablespoons rum in a small bowl. Dip each ball into the rum-butter mixture, and then roll the ball in coconut to coat completely.
Chill until firm, letting the truffles return to room temperature before serving.