Whisk together the dry rub, salt and pepper in a small mixing bowl. Season the washed and dried game hens with the rub and arrange on a sheet tray. Cover with plastic wrap and refrigerate for 1 hour.
Meanwhile, in a small saucepan over medium heat, add butter to melt. Once melted, add the shallots and saute until tender. Season with salt and pepper, to taste. Add the chicken broth and orange juice. Bring to a simmer and let reduce down to 1/2 cup, about 10 minutes. It will easily coat the back of a spoon and be slightly syrupy. Once reduced add the apple cider vinegar and hot sauce. Taste for seasoning.
Prepare your grill/smoker for indirect heat with charcoal and hickory chips. Maintain your temperature at 275 degrees F.
Arrange the game hens on the grill and cover. Smoke for 40 minutes. Remove the cover and brush the hens with the glaze, making sure to get into all the nooks and crannies. Cover the grill and smoke for an additional 15 minutes. Remove the hens from the grill, to a serving platter and let rest, covered with foil for 15 minutes before serving.