The pair had just got back from the registry office when they received SOS to help a red kite.
The Yorkshire Dales-based charity says it is becoming known as an "emergency service" for wildlife in need.
Phil Ounsley died, aged 56, while hiking on Pen-y-ghent in North Yorkshire, his daughter says.
Volunteers and paramedics helped the fell runner taken ill in the Yorkshire Dales over the weekend.
The man was part of a group of cavers exploring Diccan Pot, near Horton in Ribblesdale.
It is illegal to intentionally snare badgers under the Protection of Badgers Act 1992, police say.
Two men in their 50s have died within two weeks of each other on the famous Yorkshire walking route.
The 50-year-old man was treated on Pen-y-ghent by an off-duty paramedic but died at the scene.
Richard Sunter's relatives describe him as "loyal, strong and always there to help".
