Forget the box, you just need a web browser plugin. It could sit in the background. It could have two lists (updated occasionally like spamblockers do it), one of search engines and one of spook-luring phrases. Every, say rand(1..10) minutes, it could make a few connected queries from list B to some engine in list A. Visit a link or two from the gotten page. Stop after say rand(1..10) queries total on that theme. Throw everything away and go back to sleep.

If a million people installed this plugin, that would avg 5 queries every 5 minutes, that would be avg 1.4e9 queries per day, a tiny fraction of the intertubes.

edit: but, apology to parent, you'd never sell a browser plugin...