Remove the treads from the soles of a pair of dress shoes using a belt sander.
Cut out two pieces of scrap leather, each slightly larger than the sole of one of the shoes. Old leather coats from thrift stores are a good source of scrap; jacket pocket pieces should be just about the right size.
Melt wax with an electric heat gun and spread it onto one side of the leather pieces. Heat the wax again once on the leather and rub it into the leather until it takes on a dark and wet look. This indicates that there is enough wax in the leather to seal it.
Turn over the leather pieces and use your heat gun to melt a hot glue stick. Spread the glue all over the surface of the leather, reheating as necessary to make the glue flow. The leather should be soaked with glue by the end of this process.
Spread a thinner layer of glue on the prepared soles of the shoes.
Apply the heat gun to both the sole of the shoe and the leather until the glue is thoroughly melted and sticky, then press the shoes down onto the leather pieces.
Press down on the leather with your thumb and stroke outwards towards the edges of the shoe. This will squeeze out air bubbles and flatten the leather down.
Gently pull on the edges of the leather pieces to stretch them a little before the glue fully sets.
Put the shoes in a cold place; either a refrigerator or outside (if it is winter). This will set the glue hard.
Trim the leather to match the edges of the shoes using a sharp utility knife.
Add another layer of wax to the leather to compensate for that which melted from the heat of gluing. The shoes are now ready to dance on but shouldn't be worn outside