That's actually an easy design problem, but building it from commonly available parts requires a little ingenuity.
Get an ordinary lever like the kind used on flat bar bikes. A small BMX lever would work fine. Mount the lever on a dowel, mount a cable housing anchor on the lever, run the cable through the cable stop and anchor it to the far side of the dowel. Cut away everything that gets in the way. When you squeeze the lever, the cable housing follows it back toward the far end moving the cable out through the housing. It's harder for me to describe than to visualize, but sadly I have no graphics capability.
The other thing that would work is if you took the lever and reversed it in the body. That might be easy to do with some levers, but you would need to hold it open or rig some kind of spring to hold it open.
When you squeeze the lever, it will open the caliper.