Short term I'd try a squirt with something like this. Then use some silicone grease on the connector to keep water out and avoid further oxidation. Might get you away. Deoxidiser and silicone grease are always in my tool box.
Sounds the job - must get a tin to try but the price!! - cheaper anywhere else?
A couple of auctions have just finished on Ebay at £11.25 plus £3 odd postage. It's expensive, but it's expensive for a good reason.