If the puck is a valuable collectible, perhaps signed by a famous hockey star, then do not change its condition, because that would reduce its value. Wrap it in black tulle, or Crepeline, a fine-mesh French silk organdy fabric that is almost invisible.
Or, if it is just a decorative accent to the presentation, then screw it from the back with a fender washer under the head of the screw.
Or, if it is to be attached on the fabric of the jersey, sew a circular backer through the jersey and the backing board, and attach the puck to that. In any case, I suggest using no adhesive on the puck, since a mechanical attachment would be less invasive, stronger, and more durable.