How about hanging? A properly-conducted hanging is easy, simple, quick, and relatively painless. It doesn’t take much skill or practice, doesn’t require medical personnel, nor dealing with firearms, nor dealing with sophisticated equipment. Just a sufficiently-long length of rope, a horizontal beam, and enough room to drop to make it effective.
Dogs are being put down every day so I don’t understand how they can be out of the chemical. Or would it be politically incorrect to use the same chemical. I can hear the whining now.