ssddx, Your solution was removed at the request of the OP(Accidentally pressed the best solution button).
I recommend checking the local computer stores to see if they have the 3 pin plastic part from an old system that is ready to be tossed. Even an old pc speaker cable will work(and is easy to cut/file down to 3 pins).
The actual connectors are rather easy to remove from these types of connectors.
You just lift the small tab with a screw driver or exacto(utility) knife. No not lift too much as the tabs can break.
At that point the wire and connector slides right out and can be slid into a new connector. The down side to this is that you need to find another connector.
I can not recommend running the 2 connectors bare as they can short out. In a pinch you may be able to tape or shrink them to avoid this, but finding and old pc speaker or other set of connectors from a computer should not be too hard.