I will be chaotic good or chaotic neutral..
Go play an action or shooter game ... this is a role playing game! It ain't about killing all the people ... Assassins kill their targets for a reason, and that doesn't make them evil everytime, they can assassinate an evil person to help the good people...
Even the evil people don't just kill with no reason at all ...
You are just not a role player...
I guess people like to see Assassins as just being evil just because they kill people for a living. When they're not killing people they can still be good, and help people. That's pretty much how I played my Oblivion character, and how I'll play my Skyrim character.
Yeah he'll join the Dark Brotherhood but it'll be mostly for the money/items, and other advantages. Though outside of the brotherhood he'll be a pretty nice/good guy.
When its all said and done, an Assassin can be any alignment, even lawful good(depending on who they're working for).