In deciding what to replace with, I decided on a lever mixer, but wasn't sure about that because of the limited space, and felt it was going to impinge upon my washing machine. Conventional household mixers, I thought were just a bit to big. Then I came across these tiny mixers in my chandler store in NZ. Instantly, I knew they would do the job.
To the right, here's what that lever mixer looked like fitted.
And to the left, the tiny mixer. So much easier to turn on and off and get the temperature right for our shower. I don't know where else you could get these; try your local chandler or plumber supplies.