I used a baking soda+water mix to clean off the existing damage. I'll need to get my friend to help with removing the battery, at the least.
After I cleaned with rubbing alcohol.
I let dry and then I tested and the game seems to still function just fine aside from of course not saving. (wasn't sure if there was possibly damaged traces between the RAM and ROM. Guess I will find out later when I am able to get replacement batteries.
It seemed to keep the high scores while the game was running, just not after a power off and remove test.)