A couple of notes here – first, a few Tundra Swans will lack the yellow on the bill, so if you’ve got a group with black bills, look at all of them. Tundra Swans are noticeably smaller than the other two, so if you get one with an all-black bill in the middle of a bunch of obvious Tundras, and it’s the same size, then it’s most likely a Tundra.
Second, many Trumpeters do end up with rusty staining on their head and neck, which we don’t often see with the others, but that’s environmental and will vary with where the bird’s been feeding since it last molted.