I use 1.5f caps vice batteries on my ss games. Fit right on the board, never need replacement.
GPE, or Big Daddy has them.
Only disadvantage, game needs to be turned on once a month to maintain a charge.

Fairly clean board there, you're lucky

It's OK that way, you just won't have bookkeeping data saved

While we're on the topic of corrosion, I use an aviation product called ACF-50 after cleaning.
It prevents further corrosion, and is harmless to the components. vid is right, you gtta get the
Green coating off, or the corrosion will creep around the board.

It wiil flake off easily where the corrosion exists. ACF50 can be had at Aircraft Spruce.

As Guru Vid said, remove green, clean with vinegar, rinse with water, dry for a day,
Apply ACF50. It comes in a spray can that will last forever.

Don't worry about getting it in other places, it won't hurt a thing.
I have used it for years on my plane, and pins.

I did a slide job, as Dothedoo suggests, on a Frontier. Just as he said, everything pretty much lines up by itself.