You can get a salmon net or similar at Sports Authority, Bass Pro Shop or Walmart possibly. You will find the nets in the fishing section. You may not be able to find this particular large size, but you just want to find 2 nets, as large as you can find, to place over the birds' heads and bodies so that they cannot escape.

As far as the mate, we would not mark, nor would we invite the rest of the flock over to feed. To do so, will only allow an escape by the two that you want to capture. There is no need to mark the mate as it is safe to say that if this goose is following the injured goose, it is the mate. Just keep feeding them and try to lure them into an area that you can affect a capture and they don't have a quick escape back into the water.

We can tell by the photo that the wing looks suspect, but unless we can physically see the angle that the wing is being held by lifting the wing or see the actual the injury itself, it will be very difficult to make a diagnosis. The Regal Swan