Are there any supersonic aircraft with strictly mechanical controls?
There's one I can think of immediately, and that's the granddaddy of them all, the X-1. The X-1's control system was unassisted and it had no hydraulic system. The only part of the control system that was assisted was the horizontal stabilizer, which was operated using high-pressure nitrogen gas. 

I think most of the early supersonic test airplanes were mechanically operated .