Yes we as Christians should not kill. I actually thought you were going to quote this scripture as basis for your argument:
Revelation 13:10 He that leadeth into captivity shall go into captivity. He that killeth with the sword must be killed with the sword. Here is the patience and the faith of the saints.
The only place I recall about not killing has nothing to do with murder. It says to not kill in Exodus:
Exodus 20
10But the seventh day
is the sabbath of the LORD thy God:
in it thou shalt not do any work, thou, nor thy son, nor thy daughter, thy manservant, nor thy maidservant, nor thy cattle, nor thy stranger that
is within thy gates:
11For
in six days the LORD made heaven and earth, the sea, and all that in them
is, and rested the seventh day: wherefore the LORD blessed the sabbath day, and hallowed it.
12Honour thy father and thy mother: that thy days may be long upon the land which the LORD thy God giveth thee.
13Thou shalt not kill. 14Thou shalt not commit adultery.
15Thou shalt not steal.
16Thou shalt not bear false witness against thy neighbour.
And in Leviticus it also says kill:
Leviticus 24:17 And he that killeth any man shall surely be put to death.