Great question. You can go ahead and remove the eggs. BE CAREFUL, they can explode and you do not want to be anywhere around when this happens. The smell alone will be unbelievable. Take the eggs and toss them in the water. Turtles or other predators will take care of the rest.

Do you know for sure the gender of the swans?

The pair of swans may be females and they will go through the whole nesting process including laying of eggs. Of course, the eggs will be infertile, but this might explain why the eggs did not hatch. The Regal Swan