Hello Shawnzee...
I searched a bit and still I can't find where these MRU lists are stored.
However , I found that it only keeps the last 3 search strings.
So if you want a way to temporarily get rid of your searches,
type 3 different non-existent searches , 1 each time, and it will keep the last 3 of those, instead of your real ones. It doesn't keep more than 3.
Meanwhile, I'll keep looking for a real solution, cause it's a interesting matter of privacy...