Here's the schematic. All of the action is in the top op-amp. (The second op-amp is unused. The bottom section is just for switching and is not included in the vero.)
Switching to a log pot will adjust the taper so it's quieter at lower settings, but it won't change the minimum amount of gain.
At it's lowest setting, the circuit is essentially just a buffer, so it should be unity gain with any pot. If that's too loud, you have a few options.
- Turn down the input signal
- add an input volume pot or voltage divider
- add an output volume pot or voltage divider
If the first option isn't available, the simplest thing would be to replace the 10k output pulldown with a 10k log pot, and take the output signal from the wiper. This retains your maximum gain option while also allowing you to get outputs less than unity.
If you don't want to drill another hole, you can get a similar result by removing the gain pot entirely, and replace the 100k feedback resistor (the one that parallels the gain pot) with 47k. This gives you maximum gain at all times, but you can dial down the volume with the output pot. If you get clipping or tonal changes you don't like, you can reduce the 47k as much as necessary. You may have to experiment to get the right value.