Well, you could say "That is the sissy way" and be correct, however, the sissy way to do something means to do it in a weak or effeminate (or a stereotypical girlish) way. The sissy way out is used to mean the easy way out. One with no challenge.

Yes, “out” is just idiomatic. It means exactly the same thing with or without “out”.

way out = way to resolve a problem