Along that same line is YaCy.
With Searx, you still need the regular search engines. I suspect that your traffic can still be identified, say through timing requests or from piecing together behavioral data. I haven't really dug that deep to investigate the risks.
I will give it a shot tomorrow, just to try it out. I've seen it in passing but you're the first person I've seen, in the wild, that uses it. I'll give it a test run.