dogs and cats are not native to anywhere on earth. you cannot just let them out free. they are harmful to wildlife.
the ONLY solution is educate people on how to get animals fixed so they cant reproduce so much.
and hope they are responsible to actually do it.
once animals are born, the deed has been done. if they wont take care of it, then they are a nuisance and really are better off dead. for their own sake even.
how you kill them is meaningless. animals do not have emotions, and it really dont matter if they feel any kind of pain. they are a god damn animal.