Is it proper to greet a non-Muslim with "As-Salāmu Alaykum"?

Is it proper to greet a non-Muslim with "**As-Salāmu Alaykum**" (*Peace be upon you*) or respond with "**wa alaykumu s-salāmu wa rahmatu l-lāhi wa barakātuh**" (*may peace, mercy and blessings of God be upon you*) to non-Muslims? I do not consider myself Muslim, but I find it respectful to use these greetings to Muslims. It is not much different than I would address a Christian, except the language. Similarly I use "**IN SHA' ALLAH**" as I would say "**God willing**". I don't want to offend anyone by using these greetings.