I wouldn't recommend using general construction or Formica glue for leatherwork, especially for anything you want to last or look professional. These glues typically dry rigid and inflexible, which is terrible for leather that needs to bend and move. They are also often messy and hard to clean up without damaging the surface. You should stick to glues made specifically for leather. A quality water-based contact cement like Barge, Fiebings, or Renia, or a dedicated leathercraft glue will stay flexible and give you a strong, clean bond. Save the construction glue for the workshop projects it's intended for!