Isn't that selfish and irresponsible, when you boil it down?
By relocating are you not just passing off your known nuisance animal and it's problems onto someone else when you relocate it, that assumes it actually survives? And even if it doesn't survive the relocated animal has no idea where...
As for a humane way to euthanize that is legal in most if not all areas, is a gas chamber... Gassing with CO2 or Helium is as humane as it gets IMO, and both gasses are readily available at retail stores... The 'gas chamber' can be as simple as placing the trap in big garbage bag or any other...