We looked at the photos, and the best that we can see, these are mute swans. The mottled brown/gray swans are indeed juvenile swans. Usually, swans do not interbreed between species. Not to say that it could not happen, but it would be highly unusual. Now, having said this, because Swany is now laying eggs, anything may be possible.

We would suggest that you not destroy the eggs. See if they do indeed hatch. Even though you do not want any cygnets, we would doubt that these are fertile, but it they are, it would be interesting to see what mated with Swany. However, interesting is not the reason that we are suggesting not to destroy the eggs. Swans can count and if you mess with them too early, they may double clutch, meaning that they lay another group of eggs. It takes approximately 30% of a female swan's energy/weight to produce eggs. Since Swany is an older female, her health could be significantly affected if she laid another clutch of eggs. The Regal Swan