You could set the korg to mackie MCU mode, and use those built in commands, or, route it to a generic remote, with only the only line(s) being the command(s) you want to use. This will let pass all other messages.
Simplest way would be In the generic remote – in the lower pane you could use ‘selected’ as the filter criteria, and mute as the command. Or you can specify tracks/channels by name, but the reference actually will be to the track number, meaning a change in track order will break the remote.
Or, you could route the button on the korg to a Logical Edit preset that mutes a track or tracks based on some more granular criteria.