String damper problem- help!

I play a F jazz in a jazz situation. I like to damp the strings when comping especially walking lines. However when taking a solo I want the singing undamped sound so typical of the F Jazz. I use various foam type dampers and sometimes a nut end guitar wrap as well. The issue is that it’s impossible to quickly adjust one to another during a tune. Please don’t suggest palm damping because I have tried it often and it doesn’t work for me. 1/The bridge adjust screws shred shred my skin. 2/ I have small hands and I just can’t get my thumb to do the job well.
I was hoping that one of you guys could recommend a simple method or product that could solve this problem.
Thanks