Place cherries in a small bowl, and add enough warm water to cover. Let stand until softened, about 20 minutes. Drain well, coarsely chop, and set aside.
In a medium saucepan, combine the sugar, butter, corn syrup, and salt. Place over medium heat, and cook, stirring, until sugar is dissolved and butter is melted, about 5 minutes. Whisk in the flour. Fold in the cherries. Transfer to a small bowl, cover with plastic wrap, and refrigerate until firm, about 1 hour.
Preheat oven to 375 degrees. Line baking sheets with Silpats (French nonstick baking mats); set aside.
Remove dough from refrigerator. Roll into 3/4-inch balls, and place on prepared baking sheets about 2 inches apart. Press down lightly with palm of hand to flatten slightly.
Bake, one baking sheet at a time, until golden brown, 7 to 9 minutes. Remove from oven, and let cool for about 10 seconds. Use a small offset spatula to remove one cookie from baking sheet. Wrap around a cannoli mold or the handle of a wooden spoon, to create a tube. Repeat with remaining cookies. The cookies need to be warm to shape; if they get cold, return them to the oven briefly until they are pliable.