That fits it in with the browsers of the time:
Netscape Navigator
Internet Explorer
I would guess the code name 'Alexander' came from 'Alexander the Great', who not only traveled a lot, but also conquered, just like Safari was aiming to conquer the Internet. They must have ignored the 'die young' aspect of that connotation.Safari also has the right feelings associated with it with almost everybody. Some will think "hah, killing elephants", others will think "paying people to help me watch elephants, so that they no longer need or want to kill them", but nobody (nowadays) will associate negative thoughts (exploiting the natives; killing rare animals) with it. And, apparently, there also is a link with surfing the ocean: http://en.wikipedia.org/wiki/Surfin_Safari. I think that may have led to thinking of the name, but I doubt that is strong enough to choose the name.