You can just use a simple passive S-video to Luma Chroma adapter like this
https://www.8bitclassics.com/product...a-rca-adapter/
But you can find them all over the place like on ebay or whatever.
The corrosion inside? If it's from electrolyte, it needs to be neutralized. If it's just rust, then there's nothing much you can do other than take everything apart and treat it, but that risks messing up other stuff and I would just leave it.
IIRC, the voltages the 1701/1702 were expecting are a little bit higher than what the eventual s-video spec became, so you will probably have to adjust the image a little to compensate.
"How do I get a replacement?"
You can try just taking it to a hardware store and see if they can find one, and if they can't ask for help figuring out what size you need. Then you can order it from McMaster Carr.
https://www.mcmaster.com/products/screws/
Go to a smaller HW store where they will actually talk to you.