This is a shot of the type of connector that plugs into my Oscar Controls Vortex spinner:

The problem is that the harness it's attached to (for an older Mini-PAC) has the two signal pins backwards. (When I spin it to the right, the Windows cursor goes left, etc.) For various reasons I would prefer to fix this in hardware over software, so I need to swap the blue and green wires.
Simple question: what's the best (non-destructive) way to get those wires pulled out of this sort of connector? I tried a straight pin pushing down the barb, but I don't think I got enough purchase. Is there a better tool? (Really, there has to be a better tool; the question is, what is it?) Or would I just be better off finding a couple more of those connectors (though I have no idea what size it is or what to ask for; are they standard?) and building an adapter harness?
Thanks much!
-- Chris