I like
Isaac and it sounds fine with the other names.
I don't think
Charlie can stand alone, no. Too nicknamey and cutesy, a name a grown man may not want to go by. Or may want to use a more proper name is certain situations. But I do agree, I am not a fan of
Charles but I kind of like
Charlie. I can't really think of anything else that it could be a nn for though. Sorry.
Also do to rise in the popularity it seems recently,
Charlie on it's own makes me think of a girl. I've heard of a few girls just being named
Charlie.