I don't think there is any way to do this. You can mail or contact the site owners who crawl or show your site in there search pages like similar site search or ip based site search.
Why do you want to hide your website from Alexa? If there are sites that are linking to yours that you dont think should be public, then ask those websites to remove your links...
That's the problem, I am afraid that my emails would be ignored. Also, there are websites that deleted links to my domain but Alexa still shows them there. Is here any chance that they will be removed from the list someday? I am not sure if I follow, how will blocking of their crawler help?
I guess it is useless, just ignore it ) ... and doesn't metter if you have alexa stats or not. There aren't benefits or disadvantages!