There are a couple of ways to determine the gender. The first is pulling feathers and submitting them to a lab for DNA Sequencing. This is probably the most reliable however, may be the most costly.

If the swan was more than 2 years of age, then a veterinarian could determine the gender by looking into the cloaca. If the bird is not frozen or the carcass is not totally decomposed, you can have the bird sent to a state agriculture/veterinary medical lab and they can condcut a necropsy which can also determine the gender. In fact, a veterinarian could perform a cursory necropsy and determine the gender in the same manner that a state lab could with less the hassle. Please let us know how this works out. The Regal Swan