I think I have come up with my own solution, I'll share it here to see if it will help others.
I used AutoHotKey to do this, and below is the code I used. Basically it looks for the title of your dock in LaunchBar Commander (My First Dock) in this case, and makes the mouse Right Click Button act the same as the Left Click button. It only affects the launchBar Commander dock, and other windows and programs run unaffected. Just 4 lines of code.
#IfWinActive My First Dock ;If this window is active "My First Dock"
RButton::LButton ;Makes Right Button same as Left Button, but only in LaunchBar Commander.
#IfWinActive ; This makes all other windows unaffected by the above mapping